Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | #226×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | S4×A5 |
| commutator, prime radical, hypocenter | SL(2,𝔽3)×A5 | C2 |
| Fitting | Q8 | D3×A5 |
| socle | C2×A5 | S4 |
| cosocle | SL(2,𝔽3) | C2×A5 |
| LCS | G ▷ SL(2,𝔽3)×A5 | |
| UCS | C1 ◁ C2 | |
182 conjugacy classes of subgroups; only the 10 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 10 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.
| maximal subgroup of | A5×SL(2,𝔽7), A5×SL(2,𝔽9) |
| maximal quotient of | #226×SL(2,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.