Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C13×#106 ⋊ C2 |
| Sylow | C13 ⋊ #2094 |
290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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=dg,b^2=deg,d^2=g,e^2=g,b^a=bd,c^a=ce,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg,h^c=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2094, C2×#13116366, #15892713, … |
| maximal normal subgroup of | D13×#2094, C2×#13116366, #15892713, … |
| maximal quotient of | #15767899, #15767928, #15767960, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6040);