Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C13×H(5,𝔽2) ⋊ C2 |
| Sylow | C13 ⋊ #3585 |
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|f^2=g,b^a=bf,e^a=eg,f^a=fg,h^a=h^12,f^b=fg,d^c=dg245 conjugacy classes — view the full character table.
| maximal subgroup of | #15894213, #15894214, #15894235, … |
| maximal normal subgroup of | #15894213, #15894214, #15894235, … |
| maximal quotient of | #16726490, #16726502, #16726603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19290);