Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 995328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C3×C42×C7×C9 |
| multiplicative | (ℤ/7163)ˣ, (ℤ/7511)ˣ, (ℤ/7955)ˣ, (ℤ/8255)ˣ, (ℤ/9065)ˣ, (ℤ/9657)ˣ, (ℤ/10179)ˣ, (ℤ/14326)ˣ, (ℤ/15022)ˣ, (ℤ/15910)ˣ, (ℤ/16510)ˣ, (ℤ/18130)ˣ, (ℤ/19314)ˣ, (ℤ/20358)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C23×C32×C7 |
| socle, prime radical | C23×C32×C7 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1080 conjugacy classes of subgroups.
6048 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.