Finite Group DatabasebetaFinite Group Databasebeta| order | 11880 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | ((C3⋊D3)⋊C3)⋊C2×AGL(1,𝔽11) |
| Fitting, derived, Hall | C11×H(3,𝔽3) ⋊ C23×C5 |
| Hall | D11×((C3⋊D3)⋊C3)⋊C2 ⋊ C5 |
| Hall | H(3,𝔽3)×C11⋊C5 ⋊ C23 |
| Hall | C11⋊C5 ⋊ C2×((C3⋊D3)⋊C3)⋊C2 |
| Sylow | H(3,𝔽3) ⋊ C22×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C2×C5×((C3⋊D3)⋊C3)⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×H(3,𝔽3) | C23×C5 |
| Frattini | C3 | D32×AGL(1,𝔽11) |
| socle | C3×C11 | C2×C5×D32 |
| LCS | G ▷ C11×H(3,𝔽3) | |
| UCS | C1 | |
488 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 99 |
121 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×AGL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.