Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22⋊Q8×#261 |
| Fitting | C13×C22⋊Q8 ⋊ C4 |
| Sylow | C13 ⋊ C4×C22⋊Q8 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#328, #16780656, #16780666, … |
| maximal normal subgroup of | #261×#328, #16780656, #16780666, … |
| maximal quotient of | #261×#385, #261×#387, #261×#389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20976);