Finite Group DatabasebetaFinite Group Databasebeta| order | 22080 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 360448 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C4×C5×C8×C23 |
| multiplicative | (ℤ/25051)ˣ, (ℤ/28495)ˣ, (ℤ/34071)ˣ, (ℤ/44192)ˣ, (ℤ/45428)ˣ, (ℤ/50102)ˣ, (ℤ/56990)ˣ, (ℤ/68142)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C3×C5×C23 |
| socle, prime radical | C23×C3×C5×C23 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
22080 conjugacy classes. The character table is too large to display.
| automorphism group of | C13×C41×C47 |
| outer automorphism group of | C13×C41×C47 |
Past the SmallGroups library coverage — no SmallGroups id.