Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C139 ⋊ C2 |
| Sylow | C139 ⋊ #3108 |
390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8896 |
Polycyclic presentation:
2^7,139|c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^138,h^b=h^138,f^c=fg1970 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 14594);