Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26×C5 |
| direct product | C2×C3×#67×C5⋊D5 |
| Fitting | C23×C32×C52 ⋊ C22 |
| Hall | C32×C52 ⋊ C22×D4 |
| Sylow | C52 ⋊ C22×C3×#67 |
| Sylow | C32 ⋊ C2×D4×C5⋊D5 |
4312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#67×#1043, C2×C5⋊D5×#3811, C2×#72231398 |
| maximal normal subgroup of | C2×C3×#67×#1043, C2×C5⋊D5×#3811, C2×#72231398 |
Past the SmallGroups library coverage — no SmallGroups id.