Finite Group DatabasebetaFinite Group Databasebeta| order | 8844 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic201 |
| unambiguous semidirect product | C3⋊(C11×Dic67) |
| derived, Hall | C3×C67 ⋊ C4×C11 |
| Hall | C3×C11×C67 ⋊ C4 |
| Hall | C11×C67 ⋊ Dic3 |
| Sylow | C67 ⋊ C11×Dic3 |
| Hall | C3×C11 ⋊ Dic67 |
| Sylow | C3 ⋊ C11×Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D201 |
| commutator, hypocenter | C3×C67 | C4×C11 |
| Frattini | C2 | C11×D201 |
| Fitting, socle | C2×C3×C11×C67 | C2 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
2244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×Dic603, C11×C3⋊((C67⋊C3)⋊C4), C11×C3⋊Dic201, … |
| maximal normal subgroup of | C11×C3⋊((C67⋊C3)⋊C4), C3×C11×Dic201 |
| maximal quotient of | C11×Dic603, C11×C3⋊Dic201, C3×C11×Dic201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8844, 9);