Finite Group DatabasebetaFinite Group Databasebeta| order | 8844 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C67⋊C11 |
| unambiguous semidirect product | C3⋊(C4×C67⋊C11) |
| unambiguous semidirect product | (Dic3×C67)⋊C11 |
| derived, Hall | C3×C67 ⋊ C4×C11 |
| Hall | C3×C67⋊C11 ⋊ C4 |
| Hall | Dic3×C67 ⋊ C11 |
| Sylow | C67 ⋊ C11×Dic3 |
| Sylow | C3 ⋊ C4×C67⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C67⋊C11 |
| commutator, hypocenter | C3×C67 | C4×C11 |
| Fitting, socle | C2×C3×C67 | C2×C11 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
102 conjugacy classes — view the full character table.
| maximal subgroup of | Dic9×C67⋊C11, Dic3×(C67⋊C3)⋊C11, C3×Dic3×C67⋊C11, … |
| maximal normal subgroup of | Dic3×(C67⋊C3)⋊C11, C3×Dic3×C67⋊C11 |
| maximal quotient of | Dic9×C67⋊C11, C3×Dic3×C67⋊C11, C3⋊Dic3×C67⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8844, 13);