Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×C22⋊#261 |
| Fitting | C22×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #16783583, #16783584, #16783591, … |
| maximal normal subgroup of | #16783583, #16783584, #16783591, … |
| maximal quotient of | C22⋊C4×C22⋊#261, C4⋊C4×C22⋊#261, D4×(C2×#261)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21012);