Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of ((C3⋊S4)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×((C3⋊S4)⋊C3)⋊C2 |
| Fitting | C22×C32×C4 ⋊ C2×D3 |
| derived | C22⋊H(3,𝔽3) ⋊ C22×C4 |
944 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #72222983, D4×((C3⋊S4)⋊C3)⋊C2 |
| maximal normal subgroup of | D4×((C3⋊S4)⋊C3)⋊C2 |
| maximal quotient of | #72222983 |
| automorphism group of | C5×C3⋊S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30241);