Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#433 ⋊ C2 |
| Sylow | C13 ⋊ #2924 |
402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=e,f^2=g,b^a=be,h^b=h^12,d^c=dg,h^d=h^12218 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2924, C2×#13123492, #16726693, … |
| maximal normal subgroup of | D13×#2924, C2×#13123492, #16726693, … |
| maximal quotient of | #15860415, #15860479, #15860835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13166);