Finite Group DatabasebetaFinite Group Databasebeta| order | 3300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊#3874 |
| unambiguous semidirect product | (C2×C11)⋊#3874 |
| Fitting, socle | C2×C52×C11 ⋊ D3 |
| derived, Hall | C11×C52⋊C3 ⋊ C22 |
| Hall | C52×C11 ⋊ C2×D3 |
| Hall | C52⋊C3 ⋊ C2×D11 |
| Sylow | C52 ⋊ C2×D33 |
| Sylow | C11 ⋊ C2×#3874 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊#3874 |
| commutator, cosocle, hypocenter | C11×C52⋊C3 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C11 | D3 |
| LCS | G ▷ C11×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | D7×C11⋊#3874, C2×C7×C11⋊#3874, C2×C7⋊(C11⋊#3874), … |
| maximal normal subgroup of | C2×C7×C11⋊#3874, C2×C11×C11⋊#3874 |
| maximal quotient of | D7×C11⋊#3874, C2×C7×C11⋊#3874, C2×C7⋊(C11⋊#3874), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3300, 95);