Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊D457 |
| Fitting | C22×C4×C457 ⋊ C2 |
| Sylow | C457 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
3668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416840, C8×C22⋊D457, #44416845, … |
| maximal normal subgroup of | #44416840, C8×C22⋊D457, #44416845, … |
| maximal quotient of | C4×C22⋊Dic457, C4×#20300718, C4×#20300720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 107);