Finite Group DatabasebetaFinite Group Databasebeta| order | 8844 |
| automorphism | Aut(G) order 5837040 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2211 |
| unambiguous semidirect product | C3⋊Dic737 |
| unambiguous semidirect product | C11⋊Dic201 |
| unambiguous semidirect product | C67⋊Dic33 |
| derived, Hall | C3×C11×C67 ⋊ C4 |
| Hall | C11×C67 ⋊ Dic3 |
| Hall | C3×C67 ⋊ Dic11 |
| Sylow | C67 ⋊ Dic33 |
| Hall | C3×C11 ⋊ Dic67 |
| Sylow | C11 ⋊ Dic201 |
| Sylow | C3 ⋊ Dic737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2211 |
| commutator, hypocenter | C3×C11×C67 | C4 |
| Fitting, socle | C2×C3×C11×C67 | C2 |
| LCS | G ▷ C3×C11×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,67,2|a^2=e,b^a=b^2,c^a=c^10,d^a=d^662214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic6633, C3⋊(C11⋊((C67⋊C3)⋊C4)), C3⋊Dic2211, … |
| maximal normal subgroup of | C3⋊(C11⋊((C67⋊C3)⋊C4)), C3×Dic2211, Dic4422 |
| maximal quotient of | Dic6633, C3⋊Dic2211, C3×Dic2211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8844, 11);