Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C277 ⋊ #382 |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=f,b^2=e,c^2=d,b^a=bd,c^a=ce,g^b=g^276,g^c=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981110, #47983175, #47983176, … |
| maximal normal subgroup of | #47981110, #47983175, #47983176, … |
| maximal quotient of | #47981393, #47981396, #47981423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 414);