Finite Group DatabasebetaFinite Group Databasebeta| order | 7344 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 331776 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C4×C9×C17 |
| multiplicative | (ℤ/9785)ˣ, (ℤ/10745)ˣ, (ℤ/11433)ˣ, (ℤ/11973)ˣ, (ℤ/12873)ˣ, (ℤ/13815)ˣ, (ℤ/13905)ˣ, (ℤ/15244)ˣ, (ℤ/15964)ˣ, (ℤ/17164)ˣ, (ℤ/19570)ˣ, (ℤ/21490)ˣ, (ℤ/22068)ˣ, (ℤ/22866)ˣ, (ℤ/23946)ˣ, (ℤ/25746)ˣ, (ℤ/27630)ˣ, (ℤ/27810)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C32×C17 |
| socle, prime radical | C23×C32×C17 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
540 conjugacy classes of subgroups.
7344 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.