Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×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^276,g^c=g^2762788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981598, #47981600, #47981608, … |
| maximal normal subgroup of | #47981598, #47981600, #47981608, … |
| maximal quotient of | #47982914, #47982928, #47983022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 605);