Finite Group DatabasebetaFinite Group Databasebeta| order | 8763 |
| isoclinism | isoclinic class of C127⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C127⋊C3 |
| unambiguous semidirect product | C127⋊(C3×C23) |
| unambiguous semidirect product | (C23×C127)⋊C3 |
| Fitting, socle, Hall | C23×C127 ⋊ C3 |
| derived, Sylow | C127 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C127⋊C3 |
| commutator, hypocenter | C127 | C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C127 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C23 | |
8 conjugacy classes of subgroups.
1035 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23×C127⋊C3, C23×D127⋊C3, D23×C127⋊C3, … |
| maximal normal subgroup of | C2×C23×C127⋊C3, C23×D127⋊C3, D23×C127⋊C3, … |
| maximal quotient of | C2×C23×C127⋊C3, C23×#11765917, C3×C23×C127⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8763, 1);