Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic277 |
| Sylow | C277 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
1960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985016, SD32×Dic277, #47985023, … |
| maximal normal subgroup of | #47985016, SD32×Dic277, #47985023, … |
| maximal quotient of | Q16×#14555660, #47982018, #47982064, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 644);