Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×Dic137 |
| derived, Sylow | C137 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D137 |
| commutator, hypocenter | C137 | C43 |
| Frattini | C23 | C22×D137 |
| Fitting | C2×C42×C137 | C2 |
| socle | C23×C137 | C23 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C42 | |
258 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778621, C4×C8×Dic137, #97×Dic137, … |
| maximal normal subgroup of | #31778621, C4×C8×Dic137, #97×Dic137, … |
| maximal quotient of | #95×Dic137, C4×#17983995, C4×C8×Dic137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 391);