Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #1901 |
338 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=dfg,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^5,d^b=dg,f^b=fg,h^b=h^8,h^f=h^1292 conjugacy classes — view the full character table.
| maximal subgroup of | #16781659, #16781660, #16781661, … |
| maximal normal subgroup of | #16781659, #16781660, #16781661, … |
| maximal quotient of | #16783095, #16783097, #16783100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20537);