Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#11764047 |
| derived, Sylow | C137 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10587739 |
| commutator, hypocenter | C137 | C82 |
| Frattini | C2×C4 | C2×#10587739 |
| Fitting | C2×C8×C137 | C4 |
| socle | C22×C137 | C42 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C8 | |
74 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11764047, #31795700, #31795703, … |
| maximal normal subgroup of | C16×#11764047, #31795700, #31795703, … |
| maximal quotient of | #31795611, C16×#11764047, C8×#14555513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1389);