Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213×C4 |
| direct product | C2×#7503371 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×H(3,𝔽4) |
| commutator, Frattini, cosocle | C22×C4 | C26 |
| socle | C22 | C2×#2679 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
30699 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
136 conjugacy classes — view the full character table.
| maximal quotient of | #72259568, #72259659 |
Past the SmallGroups library coverage — no SmallGroups id.