Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 573308928 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4×C9 |
| abelian | C22×C42×C92 |
| multiplicative | (ℤ/10545)ˣ, (ℤ/11248)ˣ, (ℤ/14060)ˣ, (ℤ/15984)ˣ, (ℤ/19980)ˣ, (ℤ/21090)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C32 | C24×C32 |
| socle, prime radical | C24×C32 | C22×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5727 conjugacy classes of subgroups.
5184 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.