Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#88138 |
| Fitting | C4×C13×C22⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ C4×#121 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#88138, #15868946, #15868956, … |
| maximal normal subgroup of | C8×#88138, #15868946, #15868956, … |
| maximal quotient of | C4×#11718617, C4×#11718326, C4×#11718612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7021);