Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C13×#388 ⋊ C2 |
| Sylow | C13 ⋊ #2372 |
560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=eg,c^2=e,d^2=f,b^a=be,c^a=cf,d^b=de,h^d=h^12218 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2372, C2×#13117943, #16022615, … |
| maximal normal subgroup of | D13×#2372, C2×#13117943, #16022615, … |
| maximal quotient of | #15784368, #15784444, #15784446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7617);