Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C277 ⋊ #397 |
170 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=e,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^2762782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981166, #47981168, #47982153, … |
| maximal normal subgroup of | #47981166, #47981168, #47982153, … |
| maximal quotient of | #47981412, #47981414, #47981423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 474);