Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×#196200 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#121 |
| commutator | C22×C4 | C24×C4 |
| Frattini, cosocle | C2×C42 | C25 |
| socle | C23 | C2×#386 |
| prime radical | C23×AGL(1,ℤ/8) | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
10337 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72308938 |
| maximal normal subgroup of | C2×#72308938 |
| maximal quotient of | #72309113 |
Past the SmallGroups library coverage — no SmallGroups id.