Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | D5×#64162 |
| Fitting | C24×C32×C5 ⋊ C22 |
| Hall | C32×C5 ⋊ C2×#120 |
| Sylow | C32 ⋊ D5×#120 |
| Sylow | C5 ⋊ C2×#64162 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D5×C3⋊D3 |
| commutator, socle, cosocle | C22×C32×C5 | C24 |
| Fitting | C24×C32×C5 | C22 |
| hypercenter | C24 | D5×C3⋊D3 |
| hypocenter | C32×C5 | C2×#120 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C24 | |
3972 conjugacy classes of subgroups; only the 476 normal subgroups are shown.
This group has 3972 conjugacy classes of subgroups — too many to draw. Only its 476 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C3⋊D3×#120, AGL(1,𝔽5)×#64162, #72260159 |
| maximal normal subgroup of | D5×C3⋊D3×#120, AGL(1,𝔽5)×#64162, #72260159 |
Past the SmallGroups library coverage — no SmallGroups id.