Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | D5×#64091 |
| Fitting | C32×C5×C22⋊C4 ⋊ C22 |
| Hall | C32×C5 ⋊ C2×#120 |
| Sylow | C32 ⋊ D5×#120 |
| Sylow | C5 ⋊ C2×#64091 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D5×C3⋊D3 |
| commutator, socle, cosocle | C22×C32×C5 | C24 |
| Fitting | C32×C5×C22⋊C4 | C22 |
| hypercenter | C22⋊C4 | D5×C3⋊D3 |
| hypocenter | C32×C5 | C2×#120 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
3972 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C3⋊D3×#120, AGL(1,𝔽5)×#64091, #72260217 |
| maximal normal subgroup of | D5×C3⋊D3×#120, AGL(1,𝔽5)×#64091, #72260217 |
Past the SmallGroups library coverage — no SmallGroups id.