Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D5×#6291 |
| Hall | C33×C5 ⋊ C2×D4 |
| Sylow | C33 ⋊ D4×D5 |
| Sylow | C5 ⋊ C2×#6291 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D5×C3⋊D3 |
| commutator, Fitting, socle, cosocle | C2×C33×C5 | C23 |
| hypocenter | C33×C5 | C2×D4 |
| LCS | G ▷ C2×C33×C5 ▷ C33×C5 | |
| UCS | C1 ◁ C2 | |
904 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
132 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.