Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C277 ⋊ #427 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=e,b^2=d,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^2764444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981263, #47981264, #47981268, … |
| maximal normal subgroup of | #47981263, #47981264, #47981268, … |
| maximal quotient of | #47981915, #47981930, #47981947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 587);