Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#72211626 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4 | #127 |
| commutator | C43 | C23×C4 |
| Frattini, cosocle | C2×C43 | C24 |
| socle | C25 | #392 |
| prime radical | C23×#127 | D4 |
| LCS | G ▷ C43 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ C22×C43 ◁ G | |
| LECS | G ▷ C2×C43 ▷ C23 ▷ C1 | |
15196 conjugacy classes of subgroups.
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72211666, #72216408, #72217071 |
| maximal normal subgroup of | C2×#72211666, #72216408, #72217071 |
Past the SmallGroups library coverage — no SmallGroups id.