Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×AGL(1,𝔽5)×AGL(2,𝔽3) |
| Fitting, socle | C33×C5 ⋊ C4×GL(2,𝔽3) |
| derived | C5×PSU(3,𝔽2)⋊C3 ⋊ C2×C3×C4 |
| Sylow | C5 ⋊ C3×C4×AGL(2,𝔽3) |
1158 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
165 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×AGL(1,𝔽5)×AGL(2,𝔽3) |
| maximal normal subgroup of | C2×C3×AGL(1,𝔽5)×AGL(2,𝔽3) |
| maximal quotient of | C2×C3×AGL(1,𝔽5)×AGL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.