Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#459 ⋊ C2 |
| Sylow | C13 ⋊ #3284 |
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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=g,b^2=g,c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^12,d^b=de,e^b=eg,h^b=h^12,h^c=h^12,e^d=eg149 conjugacy classes — view the full character table.
| maximal subgroup of | #15852324, #15852332, #15852339, … |
| maximal normal subgroup of | #15852324, #15852332, #15852339, … |
| maximal quotient of | #15853703, #15853718, #15853733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16243);