Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C277 ⋊ #340 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^2764444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981176, #47981177, #47981179, … |
| maximal normal subgroup of | #47981176, #47981177, #47981179, … |
| maximal quotient of | #47981002, #47981007, #47981026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 312);