Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22579856 |
| Fitting | C22×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8864 |
2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983471, #47983476, #47983587, … |
| maximal normal subgroup of | #47983471, #47983476, #47983587, … |
| maximal quotient of | C2×#31799859, C2×#31799873, C2×#31799883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1044);