Finite Group DatabasebetaFinite Group Databasebeta| order | 4968 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 399168 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C3×C9×C23 |
| multiplicative | (ℤ/6251)ˣ, (ℤ/7923)ˣ, (ℤ/8037)ˣ, (ℤ/8883)ˣ, (ℤ/10564)ˣ, (ℤ/12502)ˣ, (ℤ/15012)ˣ, (ℤ/15846)ˣ, (ℤ/16074)ˣ, (ℤ/17766)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C32×C23 |
| socle, prime radical | C23×C32×C23 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
320 conjugacy classes of subgroups.
4968 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.