Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×Dic277 |
| Sylow | C277 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8864 |
2800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982954, #99×Dic277, #47984001, … |
| maximal normal subgroup of | #47982954, #99×Dic277, #47984001, … |
| maximal quotient of | #95×Dic277, #47981389, #47981392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 399);