Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#449 ⋊ C2 |
| Sylow | C13 ⋊ #3214 |
434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^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=fg140 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3214, C2×#13125828, #16734232, … |
| maximal normal subgroup of | D13×#3214, C2×#13125828, #16734232, … |
| maximal quotient of | #15872262, #15872669, #15873486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15502);