Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D137 |
| Fitting | M32×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D137 |
| commutator, socle | C2×C137 | C22×C8 |
| Fitting | M32×C137 | C2 |
| hypercenter | M32 | D137 |
| hypocenter | C137 | C2×M32 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×D137, #31782392, #349×D137, … |
| maximal normal subgroup of | #347×D137, #31782392, #349×D137, … |
| maximal quotient of | #346×D137, M32×Dic137, #31782382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 962);