Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#20300729 |
| Sylow | C457 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
2294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#20300729, #44416868, #44416874, … |
| maximal normal subgroup of | C4×#20300729, #44416868, #44416874, … |
| maximal quotient of | C2×#28410473, C2×#28410475, C2×#28410483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 160);