Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×((C3⋊D3)⋊C3)⋊C4 |
| derived | H(3,𝔽3) ⋊ C22×C3×C4 |
| Sylow | C3×H(3,𝔽3) ⋊ C22×C4 |
537 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×(PSU(3,𝔽2)⋊C3)⋊C4, C2×C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5), C2×C3×C4×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | C2×C3×C4×((C3⋊D3)⋊C3)⋊C2 |
| maximal quotient of | C2×C3×((C3⋊D3)⋊C3)⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2320);