Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#152103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #12696 |
| commutator | C2×C42 | C23×C4 |
| Frattini, cosocle | C2×#127 | C24 |
| prime radical | C2×#60798 | C2 |
| LCS | G ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C24×C4 ◁ C23×#127 ◁ G | |
| LECS | G ▷ C2×#127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
6277 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213428, #72250910, #72250917, … |
| maximal normal subgroup of | C2×#72213428, #72250910, #72250917, … |
Past the SmallGroups library coverage — no SmallGroups id.