Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ Q8×Q16 |
336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 336 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) = 1664 |
Polycyclic presentation:
2^7,13|a^2=eg,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,f^c=fg,h^c=h^12,h^d=h^12167 conjugacy classes — view the full character table.
| maximal subgroup of | #15776606, #15776610, #15776634, … |
| maximal normal subgroup of | #15776606, #15776610, #15776634, … |
| maximal quotient of | #15879523, #15881349, #15881350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17393);