Finite Group DatabasebetaFinite Group Databasebeta| order | 15472 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D967 |
| Fitting | C8×C967 ⋊ C2 |
| derived, Sylow | C967 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D967 |
| commutator, hypocenter | C967 | C2×C8 |
| Frattini | C4 | C2×D967 |
| Fitting | C8×C967 | C2 |
| socle | C2×C967 | C2×C4 |
| prime radical | C2×D967 | C4 |
| cosocle | C4×C967 | C22 |
| LCS | G ▷ C967 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7736 |
3880 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D967, #44526060, C2×C8×D967, … |
| maximal normal subgroup of | C16×D967, #44526060, C2×C8×D967, … |
| maximal quotient of | C8×Dic967, (C2×D967)⋊C8, Dic967⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15472, 21);