Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C3⋊Dic3)⋊C27 |
| derived | C32 ⋊ C4×C27 |
| Sylow | C32⋊C27 ⋊ C4 |
65 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,b^3=d,d^3=e,f^a=f^2,g^a=g^2,f^b=fg180 conjugacy classes — view the full character table.
| maximal subgroup of | #14515763, #92206⋊C4, #92172⋊C4, … |
| maximal normal subgroup of | #14515763, #92206⋊C4, #92172⋊C4, … |
| maximal quotient of | (C3⋊(C3⋊C8))⋊C27, C2×(C3⋊Dic3)⋊C27 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 19);