Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×GL(2,𝔽3)⋊A4 |
| Fitting | C5×H(5,𝔽2) ⋊ C3×D3 |
| derived | #994 ⋊ C2×C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C5 | A4×S4 |
| commutator, cosocle, hypocenter | #994 | C2×C3×C5 |
| Frattini | C2 | C5×A4×S4 |
| Fitting | C5×H(5,𝔽2) | C3×D3 |
| LCS | G ▷ #994 | |
| UCS | C1 ◁ C2×C5 | |
200 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
145 conjugacy classes — view the full character table.
| maximal subgroup of | D5×GL(2,𝔽3)⋊A4, C5×#983⋊A4, #72277388 |
| maximal normal subgroup of | D5×GL(2,𝔽3)⋊A4, C5×#983⋊A4, #72277388 |
Past the SmallGroups library coverage — no SmallGroups id.