Finite Group DatabasebetaFinite Group Databasebeta| order | 7200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#72229544 |
| Hall | C32×C52 ⋊ C2×C4⋊C4 |
| Sylow | C52 ⋊ C2×Dic3⋊Dic3 |
| Sylow | C32 ⋊ C2×C4⋊#1043 |
1688 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×#72231400 |
| maximal normal subgroup of | C2×#626×#1043, C2×#72231398, C2×#72231400 |
Past the SmallGroups library coverage — no SmallGroups id.