Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11764047 |
| derived, Sylow | C137 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #10587739 |
| commutator, hypocenter | C137 | C2×C4×C8 |
| Frattini | C22 | C22×#10587739 |
| Fitting | C22×C4×C137 | C4 |
| socle | C23×C137 | C2×C4 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C22×C4 | |
162 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | #31795611, #31795622, #31795625, … |
| maximal normal subgroup of | #31795611, #31795622, #31795625, … |
| maximal quotient of | C2×C8×#11764047, C2×#22578244, M16×#11764047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1504);