Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D52×D9 |
| Fitting | C2×C52×C9 ⋊ C23 |
| derived, Hall | C52×C9 ⋊ C24 |
| Sylow | C52 ⋊ C23×D9 |
| Sylow | C9 ⋊ C22×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D52×D9 |
| commutator, cosocle, hypocenter | C52×C9 | C24 |
| Frattini | C3 | C2×D3×D52 |
| Fitting | C2×C52×C9 | C23 |
| socle | C2×C3×C52 | C22×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C2 | |
900 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D9×D5⋊AGL(1,𝔽5), D9×#87886, D9×#87831, … |
| maximal normal subgroup of | C2×D9×D5⋊AGL(1,𝔽5), D9×#87886, D9×#87831, … |
| maximal quotient of | D9×#87886 |
Past the SmallGroups library coverage — no SmallGroups id.