Finite Group DatabasebetaFinite Group Databasebeta| order | 10816 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3864526848 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4×C13 |
| abelian | C22×C42×C132 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C132 |
| socle, prime radical | C24×C132 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3984 conjugacy classes of subgroups.
10816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C4×C8×C132, C2×C43×C132, C23×C42×C132, … |
| maximal normal subgroup of | C22×C4×C8×C132, C2×C43×C132, C23×C42×C132, … |
| maximal quotient of | C22×C4×C8×C132, C2×C43×C132, C23×C42×C132, … |
Past the SmallGroups library coverage — no SmallGroups id.