Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #97×C277 ⋊ C2 |
| Sylow | C277 ⋊ #432 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=e,c^2=d,e^2=f,b^a=bd,c^a=cf,g^b=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981763, #47981767, #47981771, … |
| maximal normal subgroup of | #47981763, #47981767, #47981771, … |
| maximal quotient of | #47982915, #47982930, #47983021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 604);