Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C22×C8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #1391 |
166 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 40 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,e^2=g,b^a=bc,c^a=cf,f^a=fg,h^a=h^8,d^b=df,d^c=dg,h^d=h^12122 conjugacy classes — view the full character table.
| maximal subgroup of | #16777842, #16777843, #16777844, … |
| maximal normal subgroup of | #16777842, #16777843, #16777844, … |
| maximal quotient of | #16777248, #16777299, #16777341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19598);