Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×#6591514 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#120 |
| commutator, Frattini, cosocle | C24 | C26 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×D4 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
43619 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
148 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#72245412, C2×#72246231, C2×#72246265 |
| maximal subgroup of | C2×#72236702, #72311804, #72311978, … |
| maximal normal subgroup of | C2×#72236702, #72311804, #72311978, … |
Past the SmallGroups library coverage — no SmallGroups id.