Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#433 ⋊ C2 |
| Sylow | C13 ⋊ #2978 |
402 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ceg,d^b=dg,h^b=h^12,h^c=h^12206 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2978, C2×#13123897, #16727715, … |
| maximal normal subgroup of | D13×#2978, C2×#13123897, #16727715, … |
| maximal quotient of | #15861623, #15861644, #15861701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13571);