Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#10587739 |
| unambiguous semidirect product | D137⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#10587739)⋊C23 |
| Fitting | C24×C137 ⋊ C4 |
| Sylow | C137 ⋊ C22×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#10587739 |
| commutator | C2×C137 | C23×C4 |
| Frattini | C2 | C23×#10587739 |
| Fitting | C24×C137 | C4 |
| socle | C23×C137 | C2×C4 |
| hypercenter | C24 | #10587739 |
| hypocenter | C137 | C22×C22⋊C4 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ C24 | |
674 conjugacy classes of subgroups.
584 conjugacy classes — view the full character table.
| maximal subgroup of | #31795962, #31795963, #31795970, … |
| maximal normal subgroup of | #31795962, #31795963, #31795970, … |
| maximal quotient of | C22×(C2×#10587739)⋊C4, C2×C4×C22⋊#10587739, C2×#22578344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1610);