Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×D241 |
| Fitting | C4×Q8×C241 ⋊ C2 |
| Sylow | C241 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
2440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D241, #44505838, #44505872, … |
| maximal normal subgroup of | Q8⋊C8×D241, #44505838, #44505872, … |
| maximal quotient of | C4×C4⋊C4×D241, C4×#21440607, C4×Q8×Dic241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1012);