Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C277 ⋊ #460 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^2761951 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982224, #47982225, #47982229, … |
| maximal normal subgroup of | #47982224, #47982225, #47982229, … |
| maximal quotient of | #47982512, #47982524, #47982534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 746);