Finite Group DatabasebetaFinite Group Databasebeta| order | 7104 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10616832 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C42×C37 |
| multiplicative | (ℤ/15496)ˣ, (ℤ/15645)ˣ, (ℤ/16688)ˣ, (ℤ/17840)ˣ, (ℤ/20860)ˣ, (ℤ/21456)ˣ, (ℤ/23244)ˣ, (ℤ/26820)ˣ, (ℤ/31290)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C3×C37 |
| socle, prime radical | C24×C3×C37 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
996 conjugacy classes of subgroups.
7104 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.