Finite Group DatabasebetaFinite Group Databasebeta| order | 10800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 414720 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C4×C9×C25 |
| multiplicative | (ℤ/13433)ˣ, (ℤ/14345)ˣ, (ℤ/16625)ˣ, (ℤ/16761)ˣ, (ℤ/17271)ˣ, (ℤ/19089)ˣ, (ℤ/20385)ˣ, (ℤ/21375)ˣ, (ℤ/22348)ˣ, (ℤ/23625)ˣ, (ℤ/26866)ˣ, (ℤ/28690)ˣ, (ℤ/33250)ˣ, (ℤ/33522)ˣ, (ℤ/34542)ˣ, (ℤ/38178)ˣ, (ℤ/40770)ˣ, (ℤ/42750)ˣ, (ℤ/47250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C5 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C2×C3×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
810 conjugacy classes of subgroups.
10800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.