Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C13×Q16 ⋊ C2 |
| Sylow | C13 ⋊ #3172 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^12,h^c=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | #15833511, #15833515, #15833531, … |
| maximal normal subgroup of | #15833511, #15833515, #15833531, … |
| maximal quotient of | #15863471, #15867161, #15867163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15114);