Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C277 ⋊ #336 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
Polycyclic presentation:
2^6,277|a^2=d,b^2=e,d^2=f,b^a=bc,g^a=g^2764456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47980987, #47980988, #47980989, … |
| maximal normal subgroup of | #47980987, #47980988, #47980989, … |
| maximal quotient of | #47980994, #47980996, #47980998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 304);