Finite Group DatabasebetaFinite Group Databasebeta| order | 23760 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×AGL(2,𝔽3) |
| Fitting, socle | C32×C11 ⋊ C5×GL(2,𝔽3) |
| derived | C11×PSU(3,𝔽2)⋊C3 ⋊ C2×C5 |
| Hall | C11×AGL(2,𝔽3) ⋊ C5 |
| Sylow | C11 ⋊ C5×AGL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×PSU(3,𝔽2)⋊C3 | C2×C5 |
| Fitting, socle | C32×C11 | C5×GL(2,𝔽3) |
| LCS | G ▷ C11×PSU(3,𝔽2)⋊C3 | |
| UCS | C1 | |
184 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 99 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×AGL(2,𝔽3) |
| maximal normal subgroup of | AGL(1,𝔽11)×AGL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.