Finite Group DatabasebetaFinite Group Databasebeta| order | 8844 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C67⋊C3)⋊C11) |
| unambiguous semidirect product | (C67⋊C11)⋊A4 |
| unambiguous semidirect product | (C22⋊(C67⋊C3))⋊C11 |
| Fitting, socle, derived, Hall | C22×C67 ⋊ C3×C11 |
| Hall | C22×C67⋊C11 ⋊ C3 |
| Hall | C22⋊(C67⋊C3) ⋊ C11 |
| Hall | C67⋊C11 ⋊ A4 |
| Sylow | C67 ⋊ C11×A4 |
| Sylow | C22 ⋊ (C67⋊C3)⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C67 | C3×C11 |
| LCS | G ▷ C22×C67 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
3,11,2^2,67|c^a=d,d^a=cd,e^a=e^29,e^b=e^6452 conjugacy classes — view the full character table.
| maximal subgroup of | A4×(C67⋊C3)⋊C11, C3×C22⋊((C67⋊C3)⋊C11) |
| maximal normal subgroup of | A4×(C67⋊C3)⋊C11, C3×C22⋊((C67⋊C3)⋊C11) |
| maximal quotient of | C22⋊((C67⋊C9)⋊C11), C3×C22⋊((C67⋊C3)⋊C11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8844, 23);