Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | C2×C5×H(3,𝔽3) ⋊ C23 |
| derived, Hall | C5×H(3,𝔽3) ⋊ C24 |
| Sylow | H(3,𝔽3) ⋊ C23×D5 |
| Sylow | C5 ⋊ C22×((C3⋊D3)⋊C3)⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×((C3⋊D3)⋊C3)⋊C2 |
| commutator, cosocle, hypocenter | C5×H(3,𝔽3) | C24 |
| Frattini | C3 | C2×D32×D5 |
| Fitting | C2×C5×H(3,𝔽3) | C23 |
| socle | C2×C3×C5 | C2×D32 |
| LCS | G ▷ C5×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
1002 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
88 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.