Finite Group DatabasebetaFinite Group Databasebeta| order | 25704 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 82944 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C4×C7×C9×C17 |
| multiplicative | (ℤ/26359)ˣ, (ℤ/27151)ˣ, (ℤ/27859)ˣ, (ℤ/30037)ˣ, (ℤ/38583)ˣ, (ℤ/52718)ˣ, (ℤ/54302)ˣ, (ℤ/55718)ˣ, (ℤ/60074)ˣ, (ℤ/77166)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C22×C32×C7×C17 |
| socle, prime radical | C22×C32×C7×C17 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
320 conjugacy classes of subgroups.
25704 conjugacy classes. The character table is too large to display.
| automorphism group of | C43×C613, C19×C1429 |
| outer automorphism group of | C43×C613, C19×C1429 |
Past the SmallGroups library coverage — no SmallGroups id.