Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2875 |
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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=e,b^2=f,e^2=g,b^a=bg,h^b=h^12,d^c=dg308 conjugacy classes — view the full character table.
| maximal subgroup of | #15777995, #15861497, #15861501, … |
| maximal normal subgroup of | #15777995, #15861497, #15861501, … |
| maximal quotient of | #15828510, #15828512, #15828529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12936);