Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived | C3×C9 ⋊ C4×C9 |
| Sylow | #6855 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4169 |
| commutator, hypocenter | C3×C9 | C4×C9 |
| Frattini, socle, prime radical | C2×C33 | C3×D3 |
| Fitting | C2×#6855 | C2 |
| cosocle | C2×C32×C9 | C2×C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C2×C3 | |
115 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,b^3=d,e^3=g,e^a=e^2g^2,f^a=f^2,g^a=g^2,e^b=ef126 conjugacy classes — view the full character table.
| maximal subgroup of | #92158⋊C4, #14515716, #14515718, … |
| maximal normal subgroup of | #92158⋊C4, #14515716, #14515718, … |
| maximal quotient of | #14515618, C2×#11757281 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 6);