Finite Group DatabasebetaFinite Group Databasebeta| order | 20688 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 165120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C431 |
| multiplicative | (ℤ/30205)ˣ, (ℤ/33657)ˣ, (ℤ/38835)ˣ, (ℤ/44876)ˣ, (ℤ/60410)ˣ, (ℤ/67314)ˣ, (ℤ/77670)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C431 |
| socle, prime radical | C23×C3×C431 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
108 conjugacy classes of subgroups.
20688 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.