Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C13×C22⋊Q8 ⋊ C2 |
| Sylow | C13 ⋊ #2449 |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=f,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^12,h^d=h^12206 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2449, C2×#13118642, #16030452, … |
| maximal normal subgroup of | D13×#2449, C2×#13118642, #16030452, … |
| maximal quotient of | #15784917, #15785103, #15785776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 8316);