Finite Group DatabasebetaFinite Group Databasebeta| order | 28000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1536000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4×C5 |
| abelian | C4×C5×C7×C8×C25 |
| multiplicative | (ℤ/28381)ˣ, (ℤ/28741)ˣ, (ℤ/35125)ˣ, (ℤ/56762)ˣ, (ℤ/57482)ˣ, (ℤ/70250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C5 | C22×C52×C7 |
| socle, prime radical | C22×C52×C7 | C2×C4×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
616 conjugacy classes of subgroups.
28000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.