Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C4 · Schur multiplier (H2) = C34 |
| direct product | C33×C3⋊Dic3 |
| unambiguous semidirect product | C3⋊(C33×Dic3) |
| derived | C32 ⋊ C33×C4 |
| Sylow | C35 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C33 | C3⋊D3 |
| commutator, hypocenter | C32 | C33×C4 |
| Frattini | C2 | C33×C3⋊D3 |
| Fitting, socle, prime radical | C2×C35 | C2 |
| cosocle | C2×C32 | C2×C33 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C33 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C33×#622, C32×C3⋊#622, C3×C3⋊(C3⋊#622), … |
| maximal normal subgroup of | C33×#622, C32×C3⋊#622, C3×C3⋊(C3⋊#622), … |
| maximal quotient of | C33×C3⋊(C3⋊C8), C2×C33×C3⋊Dic3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 872);