Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ #520 |
294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|a^2=f,d^2=e,b^a=be,d^a=de,c^b=ce,g^b=g^276,g^c=g^276,g^d=g^2762794 conjugacy classes. The character table is too large to display.
| maximal quotient of | #47985521, #47985527, #47985532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1031);