Finite Group DatabasebetaFinite Group Databasebeta| order | 9216 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 174558466025717760 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C218×C43 |
| abelian | C24×C43×C9 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C23×C3 | C27×C3 |
| socle, prime radical | C27×C3 | C23×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1135359 conjugacy classes of subgroups.
9216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×C42×C8×C9, C23×C44×C9, C25×C43×C9, … |
| maximal normal subgroup of | C24×C42×C8×C9, C23×C44×C9, C25×C43×C9, … |
| maximal quotient of | C24×C42×C8×C9, C23×C44×C9, C25×C43×C9, … |
Past the SmallGroups library coverage — no SmallGroups id.