Finite Group DatabasebetaFinite Group Databasebeta| order | 25960 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 18560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C4×C5×C11×C59 |
| multiplicative | (ℤ/27163)ˣ, (ℤ/32455)ˣ, (ℤ/54326)ˣ, (ℤ/64910)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C5×C11×C59 |
| socle, prime radical | C22×C5×C11×C59 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
25960 conjugacy classes. The character table is too large to display.
| automorphism group of | C23×C1181 |
| outer automorphism group of | C23×C1181 |
Past the SmallGroups library coverage — no SmallGroups id.