Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#488 ⋊ C2 |
| Sylow | C13 ⋊ #3327 |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=eg,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,h^b=h^12,f^c=fg,h^c=h^12,h^d=h^12161 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3327, C2×#13127103, #16739868, … |
| maximal normal subgroup of | D13×#3327, C2×#13127103, #16739868, … |
| maximal quotient of | #15878544, #15879326, #15880222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16777);