Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q16×C547 ⋊ C2 |
| Sylow | C547 ⋊ SD32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8752 |
Polycyclic presentation:
2^5,547|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^5461922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D547, C2×#31775945, #46855431, … |
| maximal normal subgroup of | SD32×D547, C2×#31775945, #46855431, … |
| maximal quotient of | #46854801, #46854805, #46854828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 89);