Finite Group DatabasebetaFinite Group Databasebeta| order | 18624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28311552 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C42×C97 |
| multiplicative | (ℤ/40456)ˣ, (ℤ/40845)ˣ, (ℤ/43568)ˣ, (ℤ/54460)ˣ, (ℤ/56016)ˣ, (ℤ/60684)ˣ, (ℤ/70020)ˣ, (ℤ/81690)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C3×C97 |
| socle, prime radical | C24×C3×C97 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
996 conjugacy classes of subgroups.
18624 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.