Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#20300724 |
| Fitting | C2×C8×C457 ⋊ C2 |
| Sylow | C457 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
3668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416558, C4×#20300724, #44416729, … |
| maximal normal subgroup of | #44416558, C4×#20300724, #44416729, … |
| maximal quotient of | C2×#28410462, C4×#20300724, C2×#28410464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 150);