Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C13×#390 ⋊ C2 |
| Sylow | C13 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=g,b^a=be,c^a=cf,d^b=de,h^b=h^12,h^c=h^12,h^d=h^12218 conjugacy classes — view the full character table.
| maximal subgroup of | #15878625, #15878628, #15878633, … |
| maximal normal subgroup of | #15878625, #15878628, #15878633, … |
| maximal quotient of | #15784320, #15784335, #15784388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7331);