Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | AGL(1,ℤ/8)×#261 |
| Fitting | C13×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C13 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#453, #261×#454, #16799813, … |
| maximal normal subgroup of | #261×#453, #261×#454, #16799813, … |
| maximal quotient of | AGL(1,ℤ/8)×#1057, #16795210, #16795211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21265);