Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#432 ⋊ C2 |
| Sylow | C13 ⋊ #2995 |
346 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^12,c^b=ceg,d^b=dg,h^b=h^12206 conjugacy classes — view the full character table.
| maximal subgroup of | #15757308, #15757312, #15757315, … |
| maximal normal subgroup of | #15757308, #15757312, #15757315, … |
| maximal quotient of | #15861765, #15861794, #15861901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13682);