Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C277 ⋊ #458 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|a^2=f,b^a=bd,c^a=ce,g^a=g^276,e^b=ef,d^c=df2362 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985155, #47985156, #47985161, … |
| maximal normal subgroup of | #47985155, #47985156, #47985161, … |
| maximal quotient of | #47982153, #47982158, #47982164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 739);