Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C547 ⋊ C2 |
| Sylow | C547 ⋊ #99 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4376 |
Polycyclic presentation:
2^5,547|a^2=d,b^a=bc,c^a=ce,d^b=de,f^b=f^5462741 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D547, C2×#31775916, #46854973, … |
| maximal normal subgroup of | #99×D547, C2×#31775916, #46854973, … |
| maximal quotient of | #46854724, #46854726, #46854734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 60);