Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C213 |
| direct product | C2×#72216926 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#442 |
| commutator | C2×C8 | C25×C4 |
| Frattini, cosocle | C4×C8 | C26 |
| prime radical | C2×#7623112 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C4×#41 ◁ C2×#17336 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
18252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
236 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72217166 |
| maximal normal subgroup of | C2×#72217166 |
Past the SmallGroups library coverage — no SmallGroups id.