Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C277 ⋊ #446 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^276,g^c=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982004, #47982006, #47982018, … |
| maximal normal subgroup of | #47982004, #47982006, #47982018, … |
| maximal quotient of | #47983036, #47983042, #47983726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 680);