Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C221 |
| direct product | C2×#10574064 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×C22⋊C4 |
| commutator | C22 | C26×C4 |
| Frattini, cosocle | C2×C4 | C27 |
| prime radical | C22×H(7,𝔽2) | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×#585 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Only the 81989 normal subgroups are shown; non-normal subgroups are omitted.
322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72241337, #72341589, C2×#72241304 |
| maximal normal subgroup of | C2×#72241337, #72341589, C2×#72241304 |
Past the SmallGroups library coverage — no SmallGroups id.