Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C277 ⋊ #368 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=ce,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^2764438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981351, #47981352, #47981357, … |
| maximal normal subgroup of | #47981351, #47981352, #47981357, … |
| maximal quotient of | #47981239, #47981241, #47981261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 379);