Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×D4×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×C42 |
| commutator | C2×C4 | C23×C42 |
| Frattini, cosocle | C23×C4 | C25 |
| socle | C23 | C22×#95 |
| prime radical | C24×D4 | D4 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
16537 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×#2010 |
| maximal normal subgroup of | C2×D4×#2010 |
| maximal quotient of | C2×#72237270 |
Past the SmallGroups library coverage — no SmallGroups id.