Finite Group DatabasebetaFinite Group Databasebeta| order | 31344 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 250368 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C653 |
| multiplicative | (ℤ/45745)ˣ, (ℤ/50973)ˣ, (ℤ/58785)ˣ, (ℤ/58815)ˣ, (ℤ/62704)ˣ, (ℤ/67964)ˣ, (ℤ/78380)ˣ, (ℤ/91490)ˣ, (ℤ/101946)ˣ, (ℤ/117570)ˣ, (ℤ/117630)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C653 |
| socle, prime radical | C23×C3×C653 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
108 conjugacy classes of subgroups.
31344 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.