Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#22579874 |
| Fitting | C2×C42×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×#126 |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
4444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981534, #47981537, #47985715, … |
| maximal normal subgroup of | #47981534, #47981537, #47985715, … |
| maximal quotient of | C2×#31799870, C2×#31799886, C2×#31799893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1074);