Finite Group DatabasebetaFinite Group Databasebeta| order | 31360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 532710162432 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C4×C7 |
| abelian | C23×C42×C5×C72 |
| multiplicative | (ℤ/82360)ˣ, (ℤ/98832)ˣ, (ℤ/123540)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C25×C5×C72 |
| socle, prime radical | C25×C5×C72 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
30000 conjugacy classes of subgroups.
31360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.