Реализую множество с помощью хеш таблицы. Segmentation fault при первом же присвоении числа вектору

#include <iostream>
#include <fstream>
#include <string>
#include <vector>

using namespace std;

int hashC(int key, int a, int p) {
    return ((key * a) % p) % 100000;
}


int main() {
    ifstream file;
    ofstream out;
    file.open("set.in");
    out.open("set.out");

    vector<int> *hash_table = nullptr;
    hash_table = new vector<int>(100000);

    string command;
    int number;
    int size;
    int index;
    int found = 0;
    while (file >> command) {
        file >> number;
        if (command == "insert") {
            index = hashC(number, 21, 37);
            hash_table[hashC(number, 21, 37)].push_back(number);
        }

        if (command == "delete") {
            size = hash_table[hashC(number, 21, 37)].size();
            index = hashC(number, 21, 37);
            for (int i = 0; i < size; i++) {
                if (hash_table[index][i] == number) {
                    hash_table[index].erase(hash_table[index].begin() + i);
                    continue;
                }
            }
        }

        if (command == "exists") {
            index = hashC(number, 21, 37);
            size = hash_table[index].size();
            for (int i = 0; i < size; i++) {
                if (hash_table[index][i] == number) {
                    found = 1;
                    out << "true" << endl;
                    continue;
                }
            }
            if(found == 0){
                out << "false" << endl;
            }
            found = 0;
        }
    }
    delete hash_table;
    return 0;
}