Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#20300718 |
| Fitting | C22×C4×C457 ⋊ C2 |
| Sylow | C457 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
3668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416500, #44416624, C4×#20300718, … |
| maximal normal subgroup of | #44416500, #44416624, C4×#20300718, … |
| maximal quotient of | C2×#28410459, C4×#20300718, #44416632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 97);