Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4⋊C8×C139 ⋊ C2 |
| Sylow | C139 ⋊ #1586 |
182 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8896 |
Polycyclic presentation:
2^7,139|a^2=e,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^138,d^b=df,h^b=h^138,h^c=h^1381970 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 3377);