Finite Group DatabasebetaFinite Group Databasebeta| order | 13696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C107 ⋊ C2 |
| Sylow | C107 ⋊ #3364 |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6848 |
Polycyclic presentation:
2^7,107|b^2=eg,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^106,d^b=de,f^c=fg,h^d=h^1061519 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13696, 17196);