Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#10623820 |
| Hall | C32×C52 ⋊ M16 |
| Sylow | C52 ⋊ #3712 |
| Sylow | C32 ⋊ C5×#681 |
288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
390 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72260100 |
| maximal normal subgroup of | #72260100 |
Past the SmallGroups library coverage — no SmallGroups id.