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) = C25×C8 |
| abelian | C22×C5×C8×C9×C16 |
| multiplicative | (ℤ/39729)ˣ, (ℤ/40953)ˣ, (ℤ/49856)ˣ, (ℤ/51392)ˣ, (ℤ/52972)ˣ, (ℤ/54604)ˣ, (ℤ/70848)ˣ, (ℤ/75276)ˣ, (ℤ/79458)ˣ, (ℤ/81906)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4×C8 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C3×C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5772 conjugacy classes of subgroups.
23040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.