Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #1547 |
260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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=e,c^2=f,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,h^a=h^8,d^b=dg,e^b=efg,h^c=h^12,h^e=h^1274 conjugacy classes — view the full character table.
| maximal subgroup of | #16781183, #16781184, #16781187, … |
| maximal normal subgroup of | #16781183, #16781184, #16781187, … |
| maximal quotient of | #16778286, #16778288, #16778332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20022);