Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C52 · Schur multiplier (H2) = C22×C3×C5 |
| direct product | C52×A42 |
| Fitting, socle, Hall | C24×C52 ⋊ C32 |
| derived, Sylow | C24 ⋊ C32×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | A42 |
| commutator, cosocle, hypocenter | C24 | C32×C52 |
| Frattini | C1 | G |
| Fitting, socle | C24×C52 | C32 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C52 | |
328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
400 conjugacy classes. The character table is too large to display.
| derived subgroup of | #72230199, C5⋊D5×A4⋊S4, #72231257, … |
| maximal subgroup of | A42×C5⋊D5, C52×A4⋊S4, #72230199, … |
| maximal normal subgroup of | A42×C5⋊D5, C52×A4⋊S4, #72230199, … |
Past the SmallGroups library coverage — no SmallGroups id.