Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ #1762 |
388 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 100 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|a^2=e,b^2=f,c^2=e,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^8,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16781357, #16781358, #16781359, … |
| maximal normal subgroup of | #16781357, #16781358, #16781359, … |
| maximal quotient of | #16780455, #16780456, #16780461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20280);