Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #3225 |
376 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^12,f^c=fg140 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3225, C2×#13125941, #16734322, … |
| maximal normal subgroup of | D13×#3225, C2×#13125941, #16734322, … |
| maximal quotient of | #15872302, #15872691, #15873525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15615);