Finite Group DatabasebetaFinite Group Databasebeta| order | 5400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D3×#11744719 |
| Fitting, socle, derived, Hall | C33×C52 ⋊ C23 |
| Sylow | C33 ⋊ C2×D52 |
| Sylow | C52 ⋊ C2×D3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C52 | C23 |
| LCS | G ▷ C33×C52 | |
| UCS | C1 | |
1080 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D52×C3⋊D3, D3×#14268425, D3×#14268426 |
| maximal normal subgroup of | D3×D52×C3⋊D3, D3×#14268425, D3×#14268426 |
Past the SmallGroups library coverage — no SmallGroups id.