Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C277 ⋊ #343 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=cf,g^a=g^276,d^b=df2782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981170, #47981171, #47981173, … |
| maximal normal subgroup of | #47981170, #47981171, #47981173, … |
| maximal quotient of | #47981010, #47981017, #47981023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 318);