Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#20300726 |
| Fitting | C2×D4×C457 ⋊ C2 |
| Sylow | C457 ⋊ C2×D8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
2294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416857, C4×#20300726, #44416886, … |
| maximal normal subgroup of | #44416857, C4×#20300726, #44416886, … |
| maximal quotient of | C2×#28410472, C2×#28410473, C2×#28410485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 156);