Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×A4⋊AGL(1,𝔽11) |
| Fitting, socle | C23×C11 ⋊ C5×D3 |
| derived | C11×A4 ⋊ C22×C5 |
| Hall | C2×C11⋊S4 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×S4 |
| Sylow | C11 ⋊ C2×C5×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11×A4 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C23×C11 | C5×D3 |
| LCS | G ▷ C11×A4 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
58 conjugacy classes — view the full character table.
| maximal subgroup of | #72222680, C2×S4×AGL(1,𝔽11), #72248999, … |
| maximal normal subgroup of | C2×S4×AGL(1,𝔽11), #72268661 |
| maximal quotient of | #72268661, D3×A4⋊AGL(1,𝔽11) |
Past the SmallGroups library coverage — no SmallGroups id.