Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#17984178 |
| derived, Sylow | C137 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11764049 |
| commutator, hypocenter | C137 | C2×C32 |
| Frattini | C4 | C2×#11764049 |
| Fitting | C2×C4×C137 | C8 |
| socle | C22×C137 | C16 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C4 | |
34 conjugacy classes of subgroups.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17984178, #31797872, #31797874, … |
| maximal normal subgroup of | C4×#17984178, #31797872, #31797874, … |
| maximal quotient of | C4×#17984178, C22⋊#17984178, C4⋊#17984178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1655);