Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×Dic137 |
| derived, Sylow | C137 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D137 |
| commutator, hypocenter | C137 | C22×C42 |
| Frattini | C22 | C23×D137 |
| Fitting | C23×C4×C137 | C2 |
| socle | C24×C137 | C22 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C23×C4 | |
498 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #95×Dic137, C4×#17983995, #31779013, … |
| maximal normal subgroup of | #95×Dic137, C4×#17983995, #31779013, … |
| maximal quotient of | C2×C42×Dic137, C22×#17983995, C2×#22577249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 994);