Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#17984138 |
| derived, Sylow | C137 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10587739 |
| commutator, hypocenter | C137 | C2×C32 |
| Frattini | C8 | C2×#10587739 |
| Fitting | C2×C8×C137 | C4 |
| socle | C22×C137 | C16 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C8 | |
34 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17984138, #31795894, #31795896, … |
| maximal normal subgroup of | C4×#17984138, #31795894, #31795896, … |
| maximal quotient of | C4×#17984138, C22⋊#17984138, C4⋊#17984138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1479);