Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#16814532 |
| Sylow | C457 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|a^2=d,d^2=e,b^a=bc,f^a=f^4563668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416500, #44416501, #44416502, … |
| maximal normal subgroup of | #44416500, #44416501, #44416502, … |
| maximal quotient of | #44416501, #44416503, D4⋊#16814532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 59);