Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C32 |
| direct product | C32×C3⋊#157 |
| unambiguous semidirect product | C3⋊(C32×#157) |
| Fitting, socle, Sylow | C35 ⋊ C4 |
| derived | C33 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊#157 |
| commutator, hypocenter | C33 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C35 | C4 |
| prime radical | C33×C3⋊D3 | C2 |
| cosocle | C3×C3⋊D3 | C2×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C32 | |
840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D3×#157, C3×D3×C3⋊#157, C3×#10620197, … |
| maximal normal subgroup of | C32×D3×#157, C3×D3×C3⋊#157, C3×#10620197, … |
| maximal quotient of | C32×C3⋊#622, C2×C32×C3⋊#157, C32×C3⋊(C3⋊#157) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 879);