Finite Group DatabasebetaFinite Group Databasebeta| order | 30624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12042240 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C11×C29 |
| multiplicative | (ℤ/47495)ˣ, (ℤ/52923)ˣ, (ℤ/59295)ˣ, (ℤ/61065)ˣ, (ℤ/63248)ˣ, (ℤ/64216)ˣ, (ℤ/70564)ˣ, (ℤ/71512)ˣ, (ℤ/79060)ˣ, (ℤ/91944)ˣ, (ℤ/94990)ˣ, (ℤ/96324)ˣ, (ℤ/105846)ˣ, (ℤ/107268)ˣ, (ℤ/118590)ˣ, (ℤ/122130)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C11×C29 |
| socle, prime radical | C24×C3×C11×C29 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
30624 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.