Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #3336 |
342 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=g,c^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,f^c=fg,h^c=h^12185 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3336, C2×#13127198, #16741427, … |
| maximal normal subgroup of | D13×#3336, C2×#13127198, #16741427, … |
| maximal quotient of | #15879138, #15879144, #15880564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16872);