Finite Group DatabasebetaFinite Group Databasebeta| order | 3504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 27648 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C73 |
| multiplicative | (ℤ/6153)ˣ, (ℤ/6585)ˣ, (ℤ/7016)ˣ, (ℤ/7024)ˣ, (ℤ/8204)ˣ, (ℤ/8780)ˣ, (ℤ/10524)ˣ, (ℤ/10548)ˣ, (ℤ/12306)ˣ, (ℤ/13170)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C73 |
| socle, prime radical | C23×C3×C73 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
108 conjugacy classes of subgroups.
3504 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.