Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×Dic554 |
| Sylow | C277 ⋊ D4×Q8 |
280 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8864 |
2785 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982269, #47982273, #47982331, … |
| maximal normal subgroup of | #47982269, #47982273, #47982331, … |
| maximal quotient of | C22⋊C4×Dic554, D4×#17984542, D4×C4⋊Dic277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1215);