Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #3385 |
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 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=eg,b^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^12,f^c=fg197 conjugacy classes — view the full character table.
| maximal subgroup of | #15852416, #15852418, #15852461, … |
| maximal normal subgroup of | #15852416, #15852418, #15852461, … |
| maximal quotient of | #15879542, #15879575, #15881208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17418);