Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#324 ⋊ C2 |
| Sylow | C13 ⋊ #1464 |
252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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=e,c^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,e^b=ef,h^b=h^12,h^c=h^12164 conjugacy classes — view the full character table.
| maximal subgroup of | #15772300, #15772302, #15772308, … |
| maximal normal subgroup of | #15772300, #15772302, #15772308, … |
| maximal quotient of | #15751058, #15751071, #15751086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2843);