Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#152116 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #12697 |
| commutator | C2×C42 | C23×C4 |
| Frattini, cosocle | #532 | C24 |
| prime radical | C2×#60798 | C2 |
| LCS | G ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×C42 ◁ C2×#3444 ◁ G | |
| LECS | G ▷ #532 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
6033 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72292696 |
| maximal normal subgroup of | C2×#72292696 |
Past the SmallGroups library coverage — no SmallGroups id.