Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #137×#261 |
| Fitting | C13×#137 ⋊ C4 |
| Sylow | C13 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#455, #261×#456, #16799814, … |
| maximal normal subgroup of | #261×#455, #261×#456, #16799814, … |
| maximal quotient of | #137×#1057, #16795216, #16795217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21266);