Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#6864⋊C2 |
| unambiguous semidirect product | #6864⋊C22 |
| unambiguous semidirect product | (C2×#6864)⋊C2 |
| Fitting | C2×#6864 ⋊ C2 |
| derived | C27 ⋊ C22×C9 |
| Sylow | #6864 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D27⋊C3 |
| commutator, hypocenter | C27 | C22×C9 |
| Frattini | C3×C9 | C2×C3×D3 |
| Fitting | C2×#6864 | C2 |
| socle | C2×C32 | C3×D9 |
| prime radical | C2×C3×D27 | C3 |
| cosocle | C3×C27 | C22×C3 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C2×C3 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#6864⋊C2, C4⋊(#6864⋊C2), #14516039, … |
| maximal normal subgroup of | C4×#6864⋊C2, C4⋊(#6864⋊C2), #14516039, … |
| maximal quotient of | #6864⋊Q8, C4×#6864⋊C2, C4⋊(#6864⋊C2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 199);