Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D5×#6294 |
| derived, Hall | C33×C5 ⋊ C22×C4 |
| Sylow | C33 ⋊ C2×C4×D5 |
| Sylow | C5 ⋊ C2×#6294 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×#1113 |
| commutator, hypocenter | C33×C5 | C22×C4 |
| Fitting, socle, cosocle | C2×C33×C5 | C23 |
| prime radical | C2×C3×D5×C3⋊D3 | C2 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C2 | |
580 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#6294, D3×D5×#624, #72254802 |
| maximal normal subgroup of | AGL(1,𝔽5)×#6294, D3×D5×#624, #72254802 |
Past the SmallGroups library coverage — no SmallGroups id.