Finite Group DatabasebetaFinite Group Databasebeta| order | 30720 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 135291469824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C16 |
| abelian | C23×C3×C5×C162 |
| multiplicative | (ℤ/83776)ˣ, (ℤ/98328)ˣ, (ℤ/101184)ˣ, (ℤ/107712)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C82 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C82 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
39584 conjugacy classes of subgroups.
30720 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.