Elements of the group are displayed as permutations of degree 14.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
5P |
| $A_4\times A_5^2$ |
1A |
$1$ |
$1$ |
$A_4\times A_5^2$ |
1A |
1A |
1A |
$()$ |
| $A_4\times A_5^2$ |
2A |
$2$ |
$3$ |
$C_2^2\times A_5^2$ |
1A |
2A |
2A |
$(2,5)(3,4)$ |
| $A_4\times A_5^2$ |
2B |
$2$ |
$15$ |
$C_2^4:\GL(2,4)$ |
1A |
2B |
2B |
$(6,9)(8,10)$ |
| $A_4\times A_5^2$ |
2C |
$2$ |
$15$ |
$C_2^4:\GL(2,4)$ |
1A |
2C |
2C |
$(1,12)(11,14)$ |
| $A_4\times A_5^2$ |
2D |
$2$ |
$45$ |
$C_2^4\times A_5$ |
1A |
2D |
2D |
$(2,4)(3,5)(6,7)(9,10)$ |
| $A_4\times A_5^2$ |
2E |
$2$ |
$45$ |
$C_2^4\times A_5$ |
1A |
2E |
2E |
$(1,13)(2,5)(3,4)(12,14)$ |
| $A_4\times A_5^2$ |
2F |
$2$ |
$225$ |
$A_4\times C_2^4$ |
1A |
2F |
2F |
$(1,12)(6,10)(8,9)(11,14)$ |
| $A_4\times A_5^2$ |
2G |
$2$ |
$675$ |
$C_2^6$ |
1A |
2G |
2G |
$(1,11)(2,4)(3,5)(6,8)(7,9)(12,13)$ |
| $A_4\times A_5^2$ |
3A1 |
$3$ |
$4$ |
$A_5\times \GL(2,4)$ |
3A-1 |
1A |
3A-1 |
$(2,5,4)$ |
| $A_4\times A_5^2$ |
3A-1 |
$3$ |
$4$ |
$A_5\times \GL(2,4)$ |
3A1 |
1A |
3A1 |
$(2,4,5)$ |
| $A_4\times A_5^2$ |
3B |
$3$ |
$20$ |
$A_4\times \GL(2,4)$ |
3B |
1A |
3B |
$(11,13,12)$ |
| $A_4\times A_5^2$ |
3C |
$3$ |
$20$ |
$A_4\times \GL(2,4)$ |
3C |
1A |
3C |
$(6,9,7)$ |
| $A_4\times A_5^2$ |
3D1 |
$3$ |
$80$ |
$C_3\times \GL(2,4)$ |
3D-1 |
1A |
3D-1 |
$(3,4,5)(11,14,13)$ |
| $A_4\times A_5^2$ |
3D-1 |
$3$ |
$80$ |
$C_3\times \GL(2,4)$ |
3D1 |
1A |
3D1 |
$(3,5,4)(11,13,14)$ |
| $A_4\times A_5^2$ |
3E1 |
$3$ |
$80$ |
$C_3\times \GL(2,4)$ |
3E-1 |
1A |
3E-1 |
$(2,4,5)(7,10,8)$ |
| $A_4\times A_5^2$ |
3E-1 |
$3$ |
$80$ |
$C_3\times \GL(2,4)$ |
3E1 |
1A |
3E1 |
$(2,5,4)(7,8,10)$ |
| $A_4\times A_5^2$ |
3F |
$3$ |
$400$ |
$C_3^2\times A_4$ |
3F |
1A |
3F |
$(1,14,11)(6,7,9)$ |
| $A_4\times A_5^2$ |
3G1 |
$3$ |
$1600$ |
$C_3^3$ |
3G-1 |
1A |
3G-1 |
$(1,14,11)(2,4,5)(6,7,8)$ |
| $A_4\times A_5^2$ |
3G-1 |
$3$ |
$1600$ |
$C_3^3$ |
3G1 |
1A |
3G1 |
$(1,11,14)(2,5,4)(6,8,7)$ |
| $A_4\times A_5^2$ |
5A1 |
$5$ |
$12$ |
$C_5\times A_4\times A_5$ |
5A2 |
5A2 |
1A |
$(6,7,10,8,9)$ |
| $A_4\times A_5^2$ |
5A2 |
$5$ |
$12$ |
$C_5\times A_4\times A_5$ |
5A1 |
5A1 |
1A |
$(6,10,9,7,8)$ |
| $A_4\times A_5^2$ |
5B1 |
$5$ |
$12$ |
$C_5\times A_4\times A_5$ |
5B2 |
5B2 |
1A |
$(1,14,11,13,12)$ |
| $A_4\times A_5^2$ |
5B2 |
$5$ |
$12$ |
$C_5\times A_4\times A_5$ |
5B1 |
5B1 |
1A |
$(1,11,12,14,13)$ |
| $A_4\times A_5^2$ |
5C1 |
$5$ |
$144$ |
$A_4\times C_5^2$ |
5C2 |
5C2 |
1A |
$(1,11,14,12,13)(6,10,7,8,9)$ |
| $A_4\times A_5^2$ |
5C2 |
$5$ |
$144$ |
$A_4\times C_5^2$ |
5C1 |
5C1 |
1A |
$(1,14,13,11,12)(6,7,9,10,8)$ |
| $A_4\times A_5^2$ |
5D1 |
$5$ |
$144$ |
$A_4\times C_5^2$ |
5D2 |
5D2 |
1A |
$(1,14,12,11,13)(6,9,7,8,10)$ |
| $A_4\times A_5^2$ |
5D2 |
$5$ |
$144$ |
$A_4\times C_5^2$ |
5D1 |
5D1 |
1A |
$(1,12,13,14,11)(6,7,10,9,8)$ |
| $A_4\times A_5^2$ |
6A |
$6$ |
$60$ |
$C_2^2\times \GL(2,4)$ |
3B |
2A |
6A |
$(2,5)(3,4)(11,12,13)$ |
| $A_4\times A_5^2$ |
6B |
$6$ |
$60$ |
$C_2^2\times \GL(2,4)$ |
3C |
2A |
6B |
$(2,3)(4,5)(6,7,9)$ |
| $A_4\times A_5^2$ |
6C1 |
$6$ |
$60$ |
$C_2^2\times \GL(2,4)$ |
3A1 |
2B |
6C-1 |
$(3,5,4)(6,8)(7,9)$ |
| $A_4\times A_5^2$ |
6C-1 |
$6$ |
$60$ |
$C_2^2\times \GL(2,4)$ |
3A-1 |
2B |
6C1 |
$(3,4,5)(6,8)(7,9)$ |
| $A_4\times A_5^2$ |
6D1 |
$6$ |
$60$ |
$C_2^2\times \GL(2,4)$ |
3A-1 |
2C |
6D-1 |
$(2,5,4)(11,14)(12,13)$ |
| $A_4\times A_5^2$ |
6D-1 |
$6$ |
$60$ |
$C_2^2\times \GL(2,4)$ |
3A1 |
2C |
6D1 |
$(2,4,5)(11,14)(12,13)$ |
| $A_4\times A_5^2$ |
6E |
$6$ |
$300$ |
$C_2^2:C_6^2$ |
3B |
2B |
6E |
$(7,10)(8,9)(11,12,13)$ |
| $A_4\times A_5^2$ |
6F |
$6$ |
$300$ |
$C_2^2:C_6^2$ |
3C |
2C |
6F |
$(1,13)(6,8,10)(11,14)$ |
| $A_4\times A_5^2$ |
6G |
$6$ |
$900$ |
$C_2^3\times C_6$ |
3B |
2D |
6G |
$(1,13,14)(2,4)(3,5)(6,7)(9,10)$ |
| $A_4\times A_5^2$ |
6H |
$6$ |
$900$ |
$C_2^3\times C_6$ |
3C |
2E |
6H |
$(1,11)(2,3)(4,5)(6,8,10)(13,14)$ |
| $A_4\times A_5^2$ |
6I1 |
$6$ |
$900$ |
$C_2^3\times C_6$ |
3A1 |
2F |
6I-1 |
$(1,12)(3,5,4)(6,10)(8,9)(11,14)$ |
| $A_4\times A_5^2$ |
6I-1 |
$6$ |
$900$ |
$C_2^3\times C_6$ |
3A-1 |
2F |
6I1 |
$(1,12)(3,4,5)(6,10)(8,9)(11,14)$ |
| $A_4\times A_5^2$ |
6J |
$6$ |
$1200$ |
$C_6^2$ |
3F |
2A |
6J |
$(1,11,14)(2,4)(3,5)(6,9,7)$ |
| $A_4\times A_5^2$ |
6K1 |
$6$ |
$1200$ |
$C_6^2$ |
3D1 |
2B |
6K-1 |
$(3,5,4)(6,9)(8,10)(11,13,14)$ |
| $A_4\times A_5^2$ |
6K-1 |
$6$ |
$1200$ |
$C_6^2$ |
3D-1 |
2B |
6K1 |
$(3,4,5)(6,9)(8,10)(11,14,13)$ |
| $A_4\times A_5^2$ |
6L1 |
$6$ |
$1200$ |
$C_6^2$ |
3E1 |
2C |
6L-1 |
$(1,12)(2,5,4)(7,8,10)(11,14)$ |
| $A_4\times A_5^2$ |
6L-1 |
$6$ |
$1200$ |
$C_6^2$ |
3E-1 |
2C |
6L1 |
$(1,12)(2,4,5)(7,10,8)(11,14)$ |
| $A_4\times A_5^2$ |
10A1 |
$10$ |
$36$ |
$C_2\times C_{10}\times A_5$ |
5A1 |
10A3 |
2A |
$(2,5)(3,4)(6,7,8,10,9)$ |
| $A_4\times A_5^2$ |
10A3 |
$10$ |
$36$ |
$C_2\times C_{10}\times A_5$ |
5A2 |
10A1 |
2A |
$(2,5)(3,4)(6,10,7,9,8)$ |
| $A_4\times A_5^2$ |
10B1 |
$10$ |
$36$ |
$C_2\times C_{10}\times A_5$ |
5B2 |
10B3 |
2A |
$(1,14,13,12,11)(2,3)(4,5)$ |
| $A_4\times A_5^2$ |
10B3 |
$10$ |
$36$ |
$C_2\times C_{10}\times A_5$ |
5B1 |
10B1 |
2A |
$(1,12,14,11,13)(2,3)(4,5)$ |
| $A_4\times A_5^2$ |
10C1 |
$10$ |
$180$ |
$C_2^3:C_{30}$ |
5B2 |
10C3 |
2B |
$(1,13,11,12,14)(6,8)(7,9)$ |
| $A_4\times A_5^2$ |
10C3 |
$10$ |
$180$ |
$C_2^3:C_{30}$ |
5B1 |
10C1 |
2B |
$(1,12,13,14,11)(6,8)(7,9)$ |
