Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#22579869 |
| Fitting | C22×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×#124 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983552, #47983568, #47983570, … |
| maximal normal subgroup of | #47983552, #47983568, #47983570, … |
| maximal quotient of | C2×#31799867, C2×#31799892, C2×#31799903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1067);