Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C277 ⋊ #347 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^276,c^b=cf2782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981199, #47981200, #47981201, … |
| maximal normal subgroup of | #47981199, #47981200, #47981201, … |
| maximal quotient of | #47981088, #47981247, C2×#31799780 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 327);