Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #41×#10587739 |
| Fitting | #41×C137 ⋊ C4 |
| Sylow | C137 ⋊ C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#10587739 |
| commutator, socle | C2×C137 | C23×C4 |
| Frattini | C2 | C23×#10587739 |
| Fitting | #41×C137 | C4 |
| hypercenter | #41 | #10587739 |
| hypocenter | C137 | C4×#41 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C4 ◁ #41 | |
310 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #104×#10587739, #31796554, #31796826, … |
| maximal normal subgroup of | #104×#10587739, #31796554, #31796826, … |
| maximal quotient of | #117×#10587739, C4×D4×#10587739, C4×Q8×#10587739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1615);