Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic137 |
| derived, Sylow | C137 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D137 |
| commutator, hypocenter | C137 | C24×C4 |
| Frattini | C2 | C24×D137 |
| Fitting, socle | C25×C137 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C25 | |
1362 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1368);