Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| direct product | C2×#106112 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #380 |
| commutator | C22×C4 | C22×C42 |
| Frattini, cosocle | C22×C42 | C24 |
| socle | C23 | C22⋊#95 |
| prime radical | C24×D4 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C22×C42 ▷ C22 ▷ C1 | |
13045 conjugacy classes of subgroups.
208 conjugacy classes — view the full character table.
| maximal subgroup of | #72215850, #72216091, C2×#72216088 |
| maximal normal subgroup of | #72215850, #72216091, C2×#72216088 |
Past the SmallGroups library coverage — no SmallGroups id.