Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#72211373 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #1270 |
| commutator | C4×C8 | C23×C8 |
| Frattini, cosocle | #1744 | C24 |
| socle | C23 | C2×#1270 |
| prime radical | C2×#60673 | C4 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C42 ◁ C22×#1744 ◁ G | |
| LECS | G ▷ #1744 ▷ C2×C42 ▷ C22 ▷ C1 | |
5566 conjugacy classes of subgroups.
248 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72211412, #72213854, #72215396, … |
| maximal normal subgroup of | #72213854, #72215396, C2×#72213062, … |
Past the SmallGroups library coverage — no SmallGroups id.