Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C277 ⋊ #380 |
234 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=f,b^2=d,b^a=bd,c^a=ce,g^a=g^2764444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981034, #47981035, #47981046, … |
| maximal normal subgroup of | #47981034, #47981035, #47981046, … |
| maximal quotient of | #47981390, #47981394, #47981397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 409);