Finite Group DatabasebetaFinite Group Databasebeta| order | 32580 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 25920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C5×C9×C181 |
| multiplicative | (ℤ/34409)ˣ, (ℤ/35849)ˣ, (ℤ/48897)ˣ, (ℤ/68818)ˣ, (ℤ/71698)ˣ, (ℤ/97794)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C22×C3×C5×C181 |
| socle, prime radical | C22×C3×C5×C181 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
60 conjugacy classes of subgroups.
32580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32580, 19);