Finite Group DatabasebetaFinite Group Databasebeta| order | 8844 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×(C67⋊C3)⋊C4 |
| unambiguous semidirect product | (C11×Dic67)⋊C3 |
| derived, Sylow | C67 ⋊ C3×C4×C11 |
| Hall | C11×Dic67 ⋊ C3 |
| Hall | C11×C67⋊C3 ⋊ C4 |
| Hall | C11×C67 ⋊ C3×C4 |
| Hall | Dic67 ⋊ C3×C11 |
| Hall | C67⋊C3 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D67⋊C3 |
| commutator, hypocenter | C67 | C3×C4×C11 |
| Frattini | C2 | C11×D67⋊C3 |
| Fitting, socle | C2×C11×C67 | C2×C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
374 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11×(C67⋊C3)⋊C4, C11×C3⋊((C67⋊C3)⋊C4) |
| maximal normal subgroup of | C3×C11×(C67⋊C3)⋊C4 |
| maximal quotient of | C11×Dic67⋊C9, C3×C11×(C67⋊C3)⋊C4, C11×C3⋊((C67⋊C3)⋊C4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8844, 15);