Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | #347×C139 ⋊ C2 |
| Sylow | C139 ⋊ #1355 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2224 |
Polycyclic presentation:
2^7,139|a^2=d,c^2=f,d^2=e,e^2=g,b^a=bc,c^a=ce,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^138,d^c=dg1538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 2542);