Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C13×C4⋊Q8 ⋊ C2 |
| Sylow | C13 ⋊ #2023 |
326 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,e^c=eg,h^c=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | #15751704, #15751705, #15751714, … |
| maximal normal subgroup of | #15751704, #15751705, #15751714, … |
| maximal quotient of | #15765886, #15765896, #15765926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5643);