Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C547 ⋊ #103 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17504 |
Polycyclic presentation:
2^5,547|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^546,c^b=ce2744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #103×D547, C2×#31775926, #46854996, … |
| maximal normal subgroup of | #103×D547, C2×#31775926, #46854996, … |
| maximal quotient of | Q8⋊(C547⋊C8), #46854738, #46854747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 70);