Finite Group DatabasebetaFinite Group Databasebeta| order | 32970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#20268649 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C157 | C2×C3 |
| LCS | G ▷ C5×C7×C157 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5495 |
Polycyclic presentation:
2,3,5,7,157|c^a=c^4,d^a=d^6,d^b=d^2,e^b=e^121005 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32970, 43);