Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C277 ⋊ #353 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2216 |
Polycyclic presentation:
2^6,277|a^2=d,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^276,c^b=cf,d^b=def,d^c=df1945 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981312, #47981313, #47981329, … |
| maximal normal subgroup of | #47981312, #47981313, #47981329, … |
| maximal quotient of | #47981099, #47981113, #47981164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 342);