Finite Group DatabasebetaFinite Group Databasebeta| order | 6624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 22708224 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C4×C23 |
| multiplicative | (ℤ/12831)ˣ, (ℤ/14456)ˣ, (ℤ/14595)ˣ, (ℤ/14805)ˣ, (ℤ/15512)ˣ, (ℤ/15568)ˣ, (ℤ/17108)ˣ, (ℤ/19460)ˣ, (ℤ/19944)ˣ, (ℤ/20016)ˣ, (ℤ/21684)ˣ, (ℤ/21996)ˣ, (ℤ/23268)ˣ, (ℤ/25020)ˣ, (ℤ/25662)ˣ, (ℤ/29190)ˣ, (ℤ/29610)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C32×C23 |
| socle, prime radical | C24×C32×C23 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
6624 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.