Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1713 |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=df,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^c=h^12170 conjugacy classes — view the full character table.
| maximal subgroup of | #15750782, #15776326, #15776327, … |
| maximal normal subgroup of | #15750782, #15776326, #15776327, … |
| maximal quotient of | #15756699, #15762675, #15762685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4126);