Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C13×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C13 ⋊ #3155 |
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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=eg,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^12,d^c=dg,h^c=h^12164 conjugacy classes — view the full character table.
| maximal subgroup of | #15876845, #15876849, #15914392, … |
| maximal normal subgroup of | #15876845, #15876849, #15914392, … |
| maximal quotient of | #15850778, #15850785, #15850822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14995);