Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 393216 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C32 |
| abelian | C322 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C162 | C22 |
| socle, prime radical | C22 | C162 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C162 ▷ C82 ▷ C42 ▷ C22 ▷ C1 | |
177 conjugacy classes of subgroups.
1024 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C64, C2×C322, C3×C322, … |
| maximal normal subgroup of | C32×C64, C2×C322, C3×C322, … |
| maximal quotient of | C32×C64, C2×C322, C3×C322, … |
Past the SmallGroups library coverage — no SmallGroups id.