Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C4×Dic554 |
| Sylow | C277 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
4456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981490, #47981510, C2×#31799732, … |
| maximal normal subgroup of | #47981490, #47981510, C2×#31799732, … |
| maximal quotient of | C2×C4×C4⋊Dic277, C2×C4×#17984542, C42×Dic554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1014);