Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic271 |
| Sylow | C271 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
1918 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46838213, SD32×Dic271, #46838220, … |
| maximal normal subgroup of | #46838213, SD32×Dic271, #46838220, … |
| maximal quotient of | Q16×C271⋊C8, #46835215, #46835261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 644);