Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#14555522 |
| derived, Sylow | C137 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11764049 |
| commutator, hypocenter | C137 | C4×C16 |
| Frattini | C22 | C2×#11764049 |
| Fitting | C2×C4×C137 | C8 |
| socle | C22×C137 | C2×C8 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C4 | |
58 conjugacy classes of subgroups.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14555522, #31797805, #31797806, … |
| maximal normal subgroup of | C8×#14555522, #31797805, #31797806, … |
| maximal quotient of | C8×#14555522, #31797806, #31797859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1641);