Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | C2×#7682069 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C26 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
142349 conjugacy classes of subgroups.
220 conjugacy classes — view the full character table.
| maximal subgroup of | #72226708, C2×#72219280, C22×#7682069, … |
| maximal normal subgroup of | #72226708, C2×#72219280, C22×#7682069, … |
| maximal quotient of | #72219639, C2×#72231761, C2×#72232180, … |
Past the SmallGroups library coverage — no SmallGroups id.