Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 75497472 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C43 |
| abelian | C32×C42×C5×C32 |
| multiplicative | (ℤ/29585)ˣ, (ℤ/31525)ˣ, (ℤ/59170)ˣ, (ℤ/63050)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C16 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C22×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4248 conjugacy classes of subgroups.
23040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.