Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 301989888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43 |
| abelian | C2×C42×C5×C9×C16 |
| multiplicative | (ℤ/34595)ˣ, (ℤ/46155)ˣ, (ℤ/47175)ˣ, (ℤ/49232)ˣ, (ℤ/57920)ˣ, (ℤ/59200)ˣ, (ℤ/61540)ˣ, (ℤ/62900)ˣ, (ℤ/69190)ˣ, (ℤ/92310)ˣ, (ℤ/94350)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3×C8 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C22×C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8460 conjugacy classes of subgroups.
23040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.