Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C3⋊#157)) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C34 |
| unambiguous semidirect product | C3⋊(C3⋊(C3⋊#157)) |
| Fitting, socle, derived, Sylow | C35 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C35 | C4 |
| prime radical, cosocle | C33×C3⋊D3 | C2 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
904 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3^5|a^2=b,c^a=d,d^a=c^2,e^a=e^2,f^a=f^2,g^a=g^2,c^b=c^2,d^b=d^284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 881);