Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11764049 |
| unambiguous semidirect product | #10587739⋊(C2×C8) |
| Fitting | C2×C4×C137 ⋊ C8 |
| derived, Sylow | C137 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11764049 |
| commutator, hypocenter | C137 | C2×C4×C8 |
| Frattini | C2 | C22×#11764049 |
| Fitting | C2×C4×C137 | C8 |
| socle | C22×C137 | C2×C8 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C4 | |
162 conjugacy classes of subgroups.
200 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#11764049)⋊C8, #31797796, #31797797, … |
| maximal normal subgroup of | (C2×#11764049)⋊C8, #31797796, #31797797, … |
| maximal quotient of | C2×C8×#11764049, C2×#22578487, M16×#11764049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1659);