Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C2×#7631286 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | C26 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
330505 conjugacy classes of subgroups.
244 conjugacy classes — view the full character table.
| maximal subgroup of | #72225711, #72225818, #72226161, … |
| maximal normal subgroup of | #72225711, #72225818, #72226161, … |
| maximal quotient of | #72225615, #72232064, C2×#72210469, … |
Past the SmallGroups library coverage — no SmallGroups id.