Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#14268091 |
| Fitting | C2×C52×C9 ⋊ C2×C4 |
| derived, Hall | C52×C9 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×C4×D9 |
| Sylow | C9 ⋊ C2×D5⋊AGL(1,𝔽5) |
372 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×D5⋊AGL(1,𝔽5), #72247522, #72247540, … |
| maximal normal subgroup of | C2×D9×D5⋊AGL(1,𝔽5), #72247522, #72247540, … |
| maximal quotient of | #72247540 |
Past the SmallGroups library coverage — no SmallGroups id.