Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C13×C4⋊C8 ⋊ C2 |
| Sylow | C13 ⋊ #3076 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^12,f^c=fg,h^c=h^12278 conjugacy classes — view the full character table.
| maximal subgroup of | #15757791, #15757793, #15757798, … |
| maximal normal subgroup of | #15757791, #15757793, #15757798, … |
| maximal quotient of | #15862394, #15863870, #15865083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14300);