Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C22×C5×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | C22×C5×H(3,𝔽3) ⋊ C22 |
| derived, Sylow | H(3,𝔽3) ⋊ C24×C5 |
| Hall | C5×H(3,𝔽3) ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | ((C3⋊D3)⋊C3)⋊C2 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C24×C5 |
| Frattini | C3 | C22×C5×D32 |
| Fitting | C22×C5×H(3,𝔽3) | C22 |
| socle | C22×C3×C5 | D32 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22×C5 | |
1002 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
220 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C5×AGL(2,𝔽3), C22×C3×C5×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | C22×C3×C5×((C3⋊D3)⋊C3)⋊C2 |
| maximal quotient of | C22×C3×C5×((C3⋊D3)⋊C3)⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.