Finite Group DatabasebetaFinite Group Databasebeta| order | 22176 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 28798156800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3 |
| abelian | C25×C32×C7×C11 |
| multiplicative | (ℤ/55384)ˣ, (ℤ/69144)ˣ, (ℤ/71208)ˣ, (ℤ/77784)ˣ, (ℤ/78792)ˣ, (ℤ/81144)ˣ, (ℤ/83076)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
8976 conjugacy classes of subgroups.
22176 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.