Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C16×#10587739 |
| Fitting | C16×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #10587739 |
| commutator, hypocenter | C137 | C4×C16 |
| Frattini | C8 | C2×#10587739 |
| Fitting | C16×C137 | C4 |
| socle | C2×C137 | C4×C8 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C16 | |
58 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#10587739, #31795895, C2×C16×#10587739, … |
| maximal normal subgroup of | C32×#10587739, #31795895, C2×C16×#10587739, … |
| maximal quotient of | C16×#11764047, #31795703, #31795826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1433);