Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C277 ⋊ #428 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^b=g^2762782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47983375, #47983376, #47983380, … |
| maximal normal subgroup of | #47983375, #47983376, #47983380, … |
| maximal quotient of | #47981917, #47981932, #47981950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 589);