Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C2×C13×C4⋊Q8 ⋊ C2 |
| Sylow | C13 ⋊ #2858 |
752 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 197 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|b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^12,h^b=h^12,h^d=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15761968, #15761978, #15761983, … |
| maximal normal subgroup of | #15761968, #15761978, #15761983, … |
| maximal quotient of | #15794110, #15794188, #15794261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12868);