Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C277 ⋊ #381 |
218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=f,c^2=d,b^a=bd,c^a=ce,g^c=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981096, #47983083, #47983243, … |
| maximal normal subgroup of | #47981096, #47983083, #47983243, … |
| maximal quotient of | #47981389, #47981391, #47981414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 410);