Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic914 |
| Sylow | C457 ⋊ C4×Q8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14624 |
3668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416507, #44416509, C4×#20300729, … |
| maximal normal subgroup of | #44416507, #44416509, C4×#20300729, … |
| maximal quotient of | C4×C4⋊Dic457, C4×#20300720, #44416660, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 112);