Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×#338 ⋊ C2 |
| Sylow | C13 ⋊ #2091 |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=de,d^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,h^b=h^12,h^c=h^12158 conjugacy classes — view the full character table.
| maximal subgroup of | #15776245, #15776250, #15776256, … |
| maximal normal subgroup of | #15776245, #15776250, #15776256, … |
| maximal quotient of | #15767889, #15767896, #15767901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6027);