Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C277 ⋊ #408 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=e,e^2=f,b^a=bd,g^a=g^276,c^b=cf2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981287, #47981289, #47981295, … |
| maximal normal subgroup of | #47981287, #47981289, #47981295, … |
| maximal quotient of | #47981515, #47981519, #47981523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 516);