Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C226 |
| direct product | C2×#10586381 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C4 | C26 |
| commutator, Frattini, cosocle | C22 | C28 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C22 ▷ C1 | |
At least 7520 conjugacy classes of subgroups; only the 417269 normal subgroups are shown.
280 conjugacy classes. The character table is too large to display.
| maximal quotient of | C2×#72237366 |
Past the SmallGroups library coverage — no SmallGroups id.