Finite Group DatabasebetaFinite Group Databasebeta| order | 25728 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 540672 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C4×C16×C67 |
| multiplicative | (ℤ/32011)ˣ, (ℤ/41157)ˣ, (ℤ/48255)ˣ, (ℤ/51472)ˣ, (ℤ/64022)ˣ, (ℤ/64340)ˣ, (ℤ/82314)ˣ, (ℤ/96510)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C23×C3×C67 |
| socle, prime radical | C23×C3×C67 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
25728 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.