Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7134511104 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C3×C4 |
| abelian | C23×C3×C42×C9 |
| multiplicative | (ℤ/9880)ˣ, (ℤ/10360)ˣ, (ℤ/10640)ˣ, (ℤ/11544)ˣ, (ℤ/11856)ˣ, (ℤ/12432)ˣ, (ℤ/13320)ˣ, (ℤ/13680)ˣ, (ℤ/14040)ˣ, (ℤ/14820)ˣ, (ℤ/15120)ˣ, (ℤ/15540)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C25×C32 |
| socle, prime radical | C25×C32 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
15000 conjugacy classes of subgroups.
3456 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.