Finite Group DatabasebetaFinite Group Databasebeta| order | 28512 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 14929920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C9 |
| abelian | C22×C8×C92×C11 |
| multiplicative | (ℤ/31901)ˣ, (ℤ/43581)ˣ, (ℤ/45333)ˣ, (ℤ/45657)ˣ, (ℤ/58108)ˣ, (ℤ/63802)ˣ, (ℤ/87162)ˣ, (ℤ/90666)ˣ, (ℤ/91314)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32×C4 | C23×C32×C11 |
| socle, prime radical | C23×C32×C11 | C32×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1748 conjugacy classes of subgroups.
28512 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.