Finite Group DatabasebetaFinite Group Databasebeta| order | 23040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 57982058496 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C27×C43 |
| abelian | C22×C42×C5×C8×C9 |
| multiplicative | (ℤ/60680)ˣ, (ℤ/62320)ˣ, (ℤ/64240)ˣ, (ℤ/65120)ˣ, (ℤ/72816)ˣ, (ℤ/86880)ˣ, (ℤ/87600)ˣ, (ℤ/88560)ˣ, (ℤ/88800)ˣ, (ℤ/91020)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3×C4 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C22×C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
39564 conjugacy classes of subgroups.
23040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.