Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C13×#41 ⋊ C4 |
| Sylow | C13 ⋊ #2297 |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=eg,d^2=f,b^a=be,c^a=cf,h^a=h^5,h^b=h^8,h^g=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #16785364, #16785365, #16785380, … |
| maximal normal subgroup of | #16785364, #16785365, #16785380, … |
| maximal quotient of | #16791525, #16791535, C4×#11719150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20971);