Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#478 ⋊ C2 |
| Sylow | C13 ⋊ #3240 |
328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=eg,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^12,f^c=fg,h^d=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3240, C2×#13126075, #16735086, … |
| maximal normal subgroup of | D13×#3240, C2×#13126075, #16735086, … |
| maximal quotient of | #15872460, #15872663, #15873497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15749);