Finite Group DatabasebetaFinite Group Databasebeta| order | 25152 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 199680 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C16×C131 |
| multiplicative | (ℤ/31297)ˣ, (ℤ/40137)ˣ, (ℤ/40239)ˣ, (ℤ/50368)ˣ, (ℤ/53516)ˣ, (ℤ/62594)ˣ, (ℤ/80274)ˣ, (ℤ/80478)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C23×C3×C131 |
| socle, prime radical | C23×C3×C131 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
196 conjugacy classes of subgroups.
25152 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.