Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | D5×PSU(3,𝔽2)⋊C3 |
| Fitting, socle | C32×C5 ⋊ C2×SL(2,𝔽3) |
| derived | C5×PSU(3,𝔽2) ⋊ C2×C3 |
| Sylow | C5 ⋊ C2×PSU(3,𝔽2)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×PSU(3,𝔽2) | C2×C3 |
| Fitting, socle | C32×C5 | C2×SL(2,𝔽3) |
| LCS | G ▷ C5×PSU(3,𝔽2) | |
| UCS | C1 | |
100 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
40 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.