Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C277 ⋊ C2 |
| Sylow | C277 ⋊ #496 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^276,c^b=cf2776 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982457, #47982461, #47982462, … |
| maximal normal subgroup of | #47982457, #47982461, #47982462, … |
| maximal quotient of | #47982789, #47982795, #47982806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 938);