Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| direct product | SL(2,𝔽3)×SL(2,𝔽5) |
| derived | Q8×SL(2,𝔽5) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C22 | A4×A5 |
| commutator, hypocenter | Q8×SL(2,𝔽5) | C3 |
| Fitting, cosocle | C2×Q8 | C3×A5 |
| LCS | G ▷ Q8×SL(2,𝔽5) | |
| UCS | C1 ◁ C22 | |
136 conjugacy classes of subgroups; only the 13 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 13 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
63 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.