Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊(C3⋊S4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C33 |
| direct product | C4×C3⋊(C3⋊S4) |
| Fitting | C22×C32×C4 ⋊ D3 |
| derived | C32×A4 ⋊ C2×C4 |
592 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13165924, #13165926, #13165998, … |
| maximal normal subgroup of | #13165924, #13165926, #13165998, … |
| maximal quotient of | C4×C3⋊(C3⋊#226), #13173038, C4×C3⋊(C3⋊GL(2,𝔽3)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4431);