Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Fitting | C4×C8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #1274 |
168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 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=d,b^2=e,c^2=f,d^2=g,b^a=bc,e^a=ef,d^b=df,h^b=h^8,h^e=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129659, #16778909, #16778912, … |
| maximal normal subgroup of | C2×#13129659, #16778909, #16778912, … |
| maximal quotient of | #16776825, #16776830, #16776832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19333);