Finite Group DatabasebetaFinite Group Databasebeta| order | 8844 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic67⋊C11) |
| unambiguous semidirect product | (C67⋊C11)⋊Dic3 |
| unambiguous semidirect product | Dic201⋊C11 |
| derived, Hall | C3×C67 ⋊ C4×C11 |
| Hall | C3×C67⋊C11 ⋊ C4 |
| Hall | Dic201 ⋊ C11 |
| Hall | C67⋊C11 ⋊ Dic3 |
| Sylow | C67 ⋊ C11×Dic3 |
| Sylow | C3 ⋊ Dic67⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D67⋊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.
Polycyclic presentation:
2,3,11,67,2|a^2=e,b^a=b^2,d^a=d^66,d^c=d^6484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8844, 14);