Finite Group DatabasebetaFinite Group Databasebeta| order | 8844 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊(D67⋊C3) |
| unambiguous semidirect product | (C2×C11)⋊(D67⋊C3) |
| unambiguous semidirect product | (C2×C67⋊C3)⋊D11 |
| unambiguous semidirect product | (C2×D737)⋊C3 |
| Fitting, socle | C2×C11×C67 ⋊ C2×C3 |
| derived, Hall | C11×C67 ⋊ C22×C3 |
| Hall | C2×D737 ⋊ C3 |
| Hall | C11×C67⋊C3 ⋊ C22 |
| Hall | C67⋊C3 ⋊ C2×D11 |
| Sylow | C67 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ C2×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊(D67⋊C3) |
| commutator, hypocenter | C11×C67 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C67 | C2×C3 |
| LCS | G ▷ C11×C67 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C11⋊(D67⋊C3), C2×C3×C11⋊(D67⋊C3), C2×C3⋊(C11⋊(D67⋊C3)) |
| maximal normal subgroup of | C2×C3×C11⋊(D67⋊C3) |
| maximal quotient of | C2×C11⋊(D67⋊C9), D3×C11⋊(D67⋊C3), C2×C3×C11⋊(D67⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8844, 31);