Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C13×C16 ⋊ C2 |
| Sylow | C13 ⋊ #2113 |
228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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,e^2=f,f^2=g,b^a=bd,c^b=cg,h^b=h^12440 conjugacy classes — view the full character table.
| maximal subgroup of | #15750259, #15778366, #15778369, … |
| maximal normal subgroup of | #15750259, #15778366, #15778369, … |
| maximal quotient of | #15771983, #15772055, #15772123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6123);