Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C213 |
| direct product | C2×#72216906 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#442 |
| commutator | C2×C8 | C25×C4 |
| Frattini, cosocle | C4×C8 | C26 |
| socle | C23 | C22×#442 |
| prime radical | C2×#7623096 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C42 ◁ C23×#322 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
21972 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72217166, #72321180, #72322017, … |
| maximal normal subgroup of | C2×#72217166, #72321180, #72322017, … |
Past the SmallGroups library coverage — no SmallGroups id.