Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C277 ⋊ C2 |
| Sylow | C277 ⋊ #350 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^276,c^b=cf,d^b=df,g^b=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D277, C2×#31799787, #47984793, … |
| maximal normal subgroup of | #350×D277, C2×#31799787, #47984793, … |
| maximal quotient of | #47981092, #47981108, #47981121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 334);