Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1024 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C256 |
| multiplicative | (ℤ/1799)ˣ, (ℤ/2307)ˣ, (ℤ/2313)ˣ, (ℤ/3076)ˣ, (ℤ/3598)ˣ, (ℤ/4614)ˣ, (ℤ/4626)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C128 | C22×C3 |
| socle, prime radical | C22×C3 | C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
52 conjugacy classes of subgroups.
1536 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.