Finite Group DatabasebetaFinite Group Databasebeta| order | 6624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2838528 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C9×C23 |
| multiplicative | (ℤ/13395)ˣ, (ℤ/13912)ˣ, (ℤ/14288)ˣ, (ℤ/17860)ˣ, (ℤ/19896)ˣ, (ℤ/20304)ˣ, (ℤ/20868)ˣ, (ℤ/25380)ˣ, (ℤ/26790)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C24×C3×C23 |
| socle, prime radical | C24×C3×C23 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
708 conjugacy classes of subgroups.
6624 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.