Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| isoclinism | isoclinic class of D137 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D137 |
| unambiguous semidirect product | C137⋊C26 |
| unambiguous semidirect product | (C2×C137)⋊C25 |
| Fitting, socle | C25×C137 ⋊ C2 |
| derived, Sylow | C137 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D137 |
| commutator, hypocenter | C137 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C137 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #379×D137, C2×#22577258, #31789065, … |
| maximal normal subgroup of | #379×D137, C2×#22577258, #31789065, … |
| maximal quotient of | C24×C4×D137, C25×Dic137, C23×D4×D137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1387);