Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1680 |
150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=dg,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^12,h^b=h^12,e^c=eg143 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1680, C2×#13114268, #15845326, … |
| maximal normal subgroup of | D13×#1680, C2×#13114268, #15845326, … |
| maximal quotient of | #15755986, #15759081, #15759091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 3942);