Finite Group DatabasebetaFinite Group Databasebeta| order | 28800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 188743680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4 |
| abelian | C22×C32×C4×C8×C25 |
| multiplicative | (ℤ/62504)ˣ, (ℤ/62816)ˣ, (ℤ/63105)ˣ, (ℤ/67312)ˣ, (ℤ/84140)ˣ, (ℤ/86544)ˣ, (ℤ/93756)ˣ, (ℤ/108180)ˣ, (ℤ/126210)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C5 | C24×C32×C5 |
| socle, prime radical | C24×C32×C5 | C2×C4×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6840 conjugacy classes of subgroups.
28800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.