Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×D5×AGL(2,𝔽3) |
| Fitting, socle | C2×C33×C5 ⋊ C2×GL(2,𝔽3) |
| derived | C5×PSU(3,𝔽2)⋊C3 ⋊ C23×C3 |
| Sylow | C5 ⋊ C22×C3×AGL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D5×AGL(2,𝔽3) |
| commutator, cosocle, hypocenter | C5×PSU(3,𝔽2)⋊C3 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C5 | C2×GL(2,𝔽3) |
| LCS | G ▷ C5×PSU(3,𝔽2)⋊C3 | |
| UCS | C1 ◁ C2×C3 | |
2706 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 2706 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×AGL(1,𝔽5)×AGL(2,𝔽3) |
| maximal normal subgroup of | C2×C3×AGL(1,𝔽5)×AGL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.