Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | #95×D137 |
| Fitting | #95×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D137 |
| commutator | C2×C137 | C2×C42 |
| Fitting | #95×C137 | C2 |
| socle | C23×C137 | C23 |
| hypercenter | #95 | D137 |
| hypocenter | C137 | C2×#95 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ #95 | |
330 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #327×D137, #328×D137, #31779290, … |
| maximal normal subgroup of | #327×D137, #328×D137, #31779290, … |
| maximal quotient of | #95×Dic137, #31779010, #31779017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 392);