Finite Group DatabasebetaFinite Group Databasebeta| order | 30528 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 13418496 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C8×C9×C53 |
| multiplicative | (ℤ/62488)ˣ, (ℤ/65056)ˣ, (ℤ/92448)ˣ, (ℤ/93732)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C24×C3×C53 |
| socle, prime radical | C24×C3×C53 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1014 conjugacy classes of subgroups.
30528 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.