Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #1880 |
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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=f,b^2=dfg,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^12,d^b=dg,e^b=eg,f^b=fg,h^b=h^12,d^c=dg,e^c=eg,f^c=fg206 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1880, C2×#13115193, #15864269, … |
| maximal normal subgroup of | D13×#1880, C2×#13115193, #15864269, … |
| maximal quotient of | #15757503, #15757531, #15757689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4867);