Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C5 |
| direct product | C22×D9×C5⋊D5 |
| Fitting | C22×C52×C9 ⋊ C22 |
| derived, Hall | C52×C9 ⋊ C24 |
| Sylow | C52 ⋊ C23×D9 |
| Sylow | C9 ⋊ C23×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D9×C5⋊D5 |
| commutator, cosocle, hypocenter | C52×C9 | C24 |
| Frattini | C3 | C22×D3×C5⋊D5 |
| Fitting | C22×C52×C9 | C22 |
| socle | C22×C3×C52 | C2×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C22 | |
1608 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 1608 conjugacy classes of subgroups — too many to draw. Only its 281 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 900 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D9×#1043, C22×C5⋊D5×AGL(1,ℤ/9), D9×#87886, … |
| maximal normal subgroup of | C22×D9×#1043, C22×C5⋊D5×AGL(1,ℤ/9), D9×#87886, … |
Past the SmallGroups library coverage — no SmallGroups id.