Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11764040 |
| derived, Sylow | C137 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D137 |
| commutator, hypocenter | C137 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D137 |
| Fitting | C2×C42×C137 | C2 |
| socle | C23×C137 | C2×C4 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778616, #31778623, #31778625, … |
| maximal normal subgroup of | #31778616, #31778623, #31778625, … |
| maximal quotient of | C2×C8×#11764040, C2×#22577124, M16×#11764040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 495);