Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C547 ⋊ C2 |
| Sylow | C547 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8752 |
Polycyclic presentation:
2^5,547|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^546,c^b=ce,f^b=f^5464382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×D547, C2×#31775924, #46854996, … |
| maximal normal subgroup of | #102×D547, C2×#31775924, #46854996, … |
| maximal quotient of | #46854730, #46854736, #46854744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 68);