Finite Group DatabasebetaFinite Group Databasebeta| order | 24960 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 528482304 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43 |
| abelian | C2×C3×C43×C5×C13 |
| multiplicative | (ℤ/37895)ˣ, (ℤ/48495)ˣ, (ℤ/51675)ˣ, (ℤ/51728)ˣ, (ℤ/62800)ˣ, (ℤ/64660)ˣ, (ℤ/67600)ˣ, (ℤ/68900)ˣ, (ℤ/75790)ˣ, (ℤ/96990)ˣ, (ℤ/103350)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23 | C24×C3×C5×C13 |
| socle, prime radical | C24×C3×C5×C13 | C23 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5088 conjugacy classes of subgroups.
24960 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.