Finite Group DatabasebetaFinite Group Databasebeta| order | 12528 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 60963840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C24×C3×C9×C29 |
| multiplicative | (ℤ/23541)ˣ, (ℤ/29288)ˣ, (ℤ/31388)ˣ, (ℤ/37656)ˣ, (ℤ/40356)ˣ, (ℤ/43932)ˣ, (ℤ/44604)ˣ, (ℤ/47082)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C24×C32×C29 |
| socle, prime radical | C24×C32×C29 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1340 conjugacy classes of subgroups.
12528 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.