Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ #393 |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=d,b^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 | #47982117, #47982122, #47982144, … |
| maximal normal subgroup of | #47982117, #47982122, #47982144, … |
| maximal quotient of | #47981409, #47981426, #47981438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 460);