Finite Group DatabasebetaFinite Group Databasebeta| order | 25920 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 55296 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C4 |
| abelian | C4×C5×C16×C81 |
| multiplicative | (ℤ/27557)ˣ, (ℤ/32405)ˣ, (ℤ/32425)ˣ, (ℤ/55114)ˣ, (ℤ/64810)ˣ, (ℤ/64850)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8×C27 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C2×C8×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
290 conjugacy classes of subgroups.
25920 conjugacy classes. The character table is too large to display.
| automorphism group of | C17×C1621 |
| outer automorphism group of | C17×C1621 |
Past the SmallGroups library coverage — no SmallGroups id.