Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3×C5 |
| direct product | C2×C5⋊D5×#638 |
| Fitting | C23×C32×C52 ⋊ C22 |
| Hall | C32×C52 ⋊ C22×D4 |
| Sylow | C52 ⋊ C22×#638 |
| Sylow | C32 ⋊ C2×D4×C5⋊D5 |
5664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1800 |
588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4×C3⋊D3×C5⋊D5, C2×#638×#1043, C2×#72230625 |
| maximal normal subgroup of | C2×D4×C3⋊D3×C5⋊D5, C2×#638×#1043, C2×#72230625 |
Past the SmallGroups library coverage — no SmallGroups id.