Finite Group DatabasebetaFinite Group Databasebeta| order | 7776 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4755360379856486400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C310 |
| abelian | C25×C35 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
996336 conjugacy classes of subgroups.
7776 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×C35×C4, C26×C35, C25×C34×C9, … |
| maximal normal subgroup of | C24×C35×C4, C26×C35, C25×C34×C9, … |
| maximal quotient of | C24×C35×C4, C26×C35, C25×C34×C9, … |
Past the SmallGroups library coverage — no SmallGroups id.