Finite Group DatabasebetaFinite Group Databasebeta| order | 24640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 491520 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C4×C5×C7×C8×C11 |
| multiplicative | (ℤ/27347)ˣ, (ℤ/28391)ˣ, (ℤ/31595)ˣ, (ℤ/32315)ˣ, (ℤ/33935)ˣ, (ℤ/46275)ˣ, (ℤ/54694)ˣ, (ℤ/56782)ˣ, (ℤ/61700)ˣ, (ℤ/63190)ˣ, (ℤ/64630)ˣ, (ℤ/67870)ˣ, (ℤ/92550)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C5×C7×C11 |
| socle, prime radical | C23×C5×C7×C11 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
24640 conjugacy classes. The character table is too large to display.
| automorphism group of | C23×C29×C41 |
| outer automorphism group of | C23×C29×C41 |
Past the SmallGroups library coverage — no SmallGroups id.