Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #11757683 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting, Sylow | #6898 ⋊ C4 |
| derived | C92 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C92 | C3×C4 |
| Frattini, socle | C32 | C3×#157 |
| Fitting | #6898 | C4 |
| prime radical | #92312 | C2 |
| cosocle | C9⋊D9 | C2×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,d^3=f,e^3=g,d^a=deg^2,e^a=de^2g^2,f^a=fg,g^a=fg^2,d^b=dfg,e^b=efg^2,d^c=d^2f^2,e^c=e^2g^2,f^c=f^2,g^c=g^224 conjugacy classes — view the full character table.
| maximal subgroup of | #14517906, #11757683⋊C2, #14517943, … |
| maximal normal subgroup of | #14517906, #11757683⋊C2, #14517943, … |
| maximal quotient of | #14516726, C2×#11757683 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 408);