Finite Group DatabasebetaFinite Group Databasebeta| order | 28512 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 836075520 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C9 |
| abelian | C23×C4×C92×C11 |
| multiplicative | (ℤ/48507)ˣ, (ℤ/56715)ˣ, (ℤ/58904)ˣ, (ℤ/58995)ˣ, (ℤ/60344)ˣ, (ℤ/60496)ˣ, (ℤ/64676)ˣ, (ℤ/75620)ˣ, (ℤ/85752)ˣ, (ℤ/85968)ˣ, (ℤ/88356)ˣ, (ℤ/90516)ˣ, (ℤ/91908)ˣ, (ℤ/97014)ˣ, (ℤ/107460)ˣ, (ℤ/113430)ˣ, (ℤ/117990)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C32 | C24×C32×C11 |
| socle, prime radical | C24×C32×C11 | C2×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5428 conjugacy classes of subgroups.
28512 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.