Finite Group DatabasebetaFinite Group Databasebeta| order | 6336 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1209522585600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C215 |
| abelian | C26×C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C26×C3×C11 |
| socle, prime radical | C26×C3×C11 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16950 conjugacy classes of subgroups.
6336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×C4×C9×C11, C27×C9×C11, C26×C11×C27, … |
| maximal normal subgroup of | C25×C4×C9×C11, C27×C9×C11, C26×C11×C27, … |
| maximal quotient of | C25×C4×C9×C11, C27×C9×C11, C26×C11×C27, … |
Past the SmallGroups library coverage — no SmallGroups id.