Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C277 ⋊ C2 |
| Sylow | C277 ⋊ #508 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^276,d^b=de,e^b=ef,g^b=g^276,g^c=g^2761540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47985475, #47985477, #47985481, … |
| maximal normal subgroup of | #47985475, #47985477, #47985481, … |
| maximal quotient of | #47984873, #47984948, #47985013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 982);