Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#72229571 |
| Hall | C32×C52 ⋊ C2×C22⋊C4 |
| Sylow | C52 ⋊ C2×(C2×D3)⋊Dic3 |
| Sylow | C32 ⋊ C2×C22⋊#1043 |
2328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#626×#1043, C2×#72231398, C2×#72231574 |
| maximal normal subgroup of | C2×#626×#1043, C2×#72231398, C2×#72231574 |
Past the SmallGroups library coverage — no SmallGroups id.