Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #4169⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#4169⋊C3 |
| unambiguous semidirect product | (C2×#4169)⋊C3 |
| Fitting | C2×#6891 ⋊ C2 |
| derived | C3×C9 ⋊ C22×C32 |
| Sylow | #6891 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #4169⋊C3 |
| commutator, cosocle, hypocenter | C3×C9 | C22×C32 |
| Frattini | C32 | C2×C32×D3 |
| Fitting | C2×#6891 | C2 |
| socle | C2×C32 | C32×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2 | |
302 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | (#4169⋊C3)⋊C4, #10619537⋊C3, #10619536⋊C3, … |
| maximal normal subgroup of | (#4169⋊C3)⋊C4, #10619537⋊C3, #10619536⋊C3, … |
| maximal quotient of | #10619590⋊C3, C4×#4169⋊C3, C4⋊(#4169⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 606);