Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #367×C139 ⋊ C2 |
| Sylow | C139 ⋊ #2228 |
136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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=d,b^2=dg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^138,e^c=ef,f^c=fg,h^c=h^1381547 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 6666);