Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Sylow | C13 ⋊ #1450 |
212 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 133 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=e,d^2=f,e^2=g,h^a=h^12,c^b=cf320 conjugacy classes — view the full character table.
| maximal subgroup of | #15753357, #15753359, #15753361, … |
| maximal normal subgroup of | #15753357, #15753359, #15753361, … |
| maximal quotient of | #15752276, #15752305, #15753349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2794);