Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#72233908 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#1790 |
| commutator | C22×D4 | C24×C4 |
| Frattini, cosocle | C2×C4×D4 | C25 |
| prime radical | C22×#52031 | C2 |
| LCS | G ▷ C22×D4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ C23×C4×D4 ◁ G | |
| LECS | G ▷ C2×C4×D4 ▷ C23 ▷ C2 ▷ C1 | |
At least 6582 conjugacy classes of subgroups; only the 2024 normal subgroups are shown.
164 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72240196 |
| maximal normal subgroup of | C2×#72240196 |
Past the SmallGroups library coverage — no SmallGroups id.