Finite Group DatabasebetaFinite Group Databasebeta| order | 2640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×#63140⋊C5 |
| Hall | C2×#63140 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C2×D4 |
| Hall | C11⋊C5 ⋊ C2×#67 |
| Hall | C3×C11 ⋊ C2×C5×D4 |
| Sylow | C11 ⋊ C2×C5×#67 |
| Sylow | C3 ⋊ C2×C22⋊AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×AGL(1,𝔽11) |
| commutator, cosocle | C2×C3×C11 | C23×C5 |
| Frattini | C2 | C2×D3×AGL(1,𝔽11) |
| Fitting, socle | C22×C3×C11 | C22×C5 |
| hypocenter | C3×C11 | C2×C5×D4 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C22 | |
216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
102 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.