Finite Group DatabasebetaFinite Group Databasebeta| order | 8052 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic61⋊C3 |
| unambiguous semidirect product | Dic61⋊(C3×C11) |
| unambiguous semidirect product | (C11×Dic61)⋊C3 |
| derived, Sylow | C61 ⋊ C3×C4×C11 |
| Hall | C11×Dic61 ⋊ C3 |
| Hall | C11×C61⋊C3 ⋊ C4 |
| Hall | C11×C61 ⋊ C3×C4 |
| Hall | Dic61 ⋊ C3×C11 |
| Hall | C61⋊C3 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D61⋊C3 |
| commutator, hypocenter | C61 | C3×C4×C11 |
| Frattini | C2 | C11×D61⋊C3 |
| Fitting, socle | C2×C11×C61 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
352 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11×Dic61⋊C3, C11×C3⋊(Dic61⋊C3) |
| maximal normal subgroup of | C3×C11×Dic61⋊C3 |
| maximal quotient of | C11×Dic61⋊C9, C3×C11×Dic61⋊C3, C11×C3⋊(Dic61⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8052, 10);