Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#470 ⋊ C2 |
| Sylow | C13 ⋊ #3349 |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=g,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^12,h^d=h^12125 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3349, C2×#13127361, #16741575, … |
| maximal normal subgroup of | D13×#3349, C2×#13127361, #16741575, … |
| maximal quotient of | #15879247, #15879277, #15880606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17035);