Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic274 |
| Sylow | C137 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D137 |
| commutator | C2×C137 | C25 |
| Frattini | C2 | C24×D137 |
| Fitting | C23×C4×C137 | C2 |
| socle | C24×C137 | C22 |
| hypercenter | C23×C4 | D137 |
| hypocenter | C137 | C23×Q8 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
850 conjugacy classes of subgroups.
2216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779059, #31780712, #31780723, … |
| maximal normal subgroup of | #31779059, #31780712, #31780723, … |
| maximal quotient of | C23×#14555489, C23×C4⋊Dic137, C22×C4×Dic274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1373);