Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C277 ⋊ C2 |
| Sylow | C277 ⋊ #407 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|a^2=e,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 | #47981102, #47983086, #47983089, … |
| maximal normal subgroup of | #47981102, #47983086, #47983089, … |
| maximal quotient of | #47981493, #47981496, #47981499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 512);