Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #100×C277 ⋊ C2 |
| Sylow | C277 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2216 |
Polycyclic presentation:
2^6,277|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^276,d^b=de,g^b=g^276,d^c=df1531 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×D277, C2×#31799790, #47984807, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D277, C2×#31799790, #47984807, … |
| maximal quotient of | #47981094, #47981116, #47981165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 337);