Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#496 ⋊ C2 |
| Sylow | C13 ⋊ #3403 |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=e,c^2=eg,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^12,h^d=h^12125 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3403, C2×#13127921, #16743953, … |
| maximal normal subgroup of | D13×#3403, C2×#13127921, #16743953, … |
| maximal quotient of | #15879800, #15879804, #15881799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17595);