Finite Group DatabasebetaFinite Group Databasebeta| order | 8844 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊((C67⋊C3)⋊C4) |
| unambiguous semidirect product | (C67⋊C3)⋊Dic11 |
| unambiguous semidirect product | Dic737⋊C3 |
| derived, Hall | C11×C67 ⋊ C3×C4 |
| Hall | Dic737 ⋊ C3 |
| Hall | C11×C67⋊C3 ⋊ C4 |
| Hall | C67⋊C3 ⋊ Dic11 |
| Sylow | C67 ⋊ C3×Dic11 |
| Sylow | C11 ⋊ (C67⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(D67⋊C3) |
| commutator, hypocenter | C11×C67 | C3×C4 |
| Fitting, socle | C2×C11×C67 | C2×C3 |
| LCS | G ▷ C11×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,67,2|a^2=e,c^a=c^10,d^a=d^66,d^b=d^37284 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11⋊((C67⋊C3)⋊C4), C3⋊(C11⋊((C67⋊C3)⋊C4)) |
| maximal normal subgroup of | C3×C11⋊((C67⋊C3)⋊C4) |
| maximal quotient of | C11⋊(Dic67⋊C9), C3×C11⋊((C67⋊C3)⋊C4), C3⋊(C11⋊((C67⋊C3)⋊C4)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8844, 17);