Finite Group DatabasebetaFinite Group Databasebeta| order | 5400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | D52×C3⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C33×C52 ⋊ C23 |
| Sylow | C33 ⋊ C2×D52 |
| Sylow | C52 ⋊ C22×C3⋊(C3⋊D3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C52 | C23 |
| LCS | G ▷ C33×C52 | |
| UCS | C1 | |
2072 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 298 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 270 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊(C3⋊D3)×D5⋊AGL(1,𝔽5), D3×D52×C3⋊D3, #72247781 |
| maximal normal subgroup of | C3⋊(C3⋊D3)×D5⋊AGL(1,𝔽5), D3×D52×C3⋊D3, #72247781 |
Past the SmallGroups library coverage — no SmallGroups id.