Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C547 ⋊ C2 |
| Sylow | C547 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8752 |
Polycyclic presentation:
2^5,547|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^546,d^b=de,f^c=f^5461922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #137×D547, C2×#31776034, #46855798, … |
| maximal normal subgroup of | #137×D547, C2×#31776034, #46855798, … |
| maximal quotient of | #46855001, #46855008, #46855042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 178);