Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C13×#497 ⋊ C2 |
| Sylow | C13 ⋊ #3153 |
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|b^2=e,c^2=fg,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^c=h^12,h^d=h^12128 conjugacy classes — view the full character table.
| maximal subgroup of | #15783211, #15844136, #15844144, … |
| maximal normal subgroup of | #15783211, #15844136, #15844144, … |
| maximal quotient of | #15850779, #15850794, #15850823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14973);