Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C277 ⋊ C2 |
| Sylow | C277 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^276,d^b=de,e^b=ef,g^b=g^2762776 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985064, #47985067, #47985114, … |
| maximal normal subgroup of | #47985064, #47985067, #47985114, … |
| maximal quotient of | #47984880, #47984884, #47984955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 987);