Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D547)⋊C4 |
| Fitting | C22⋊C4×C547 ⋊ C2 |
| Sylow | C547 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8752 |
Polycyclic presentation:
2^5,547|a^2=e,c^2=e,b^a=bd,f^c=f^5462750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D4×D547, C2×(C22⋊D547)⋊C4, C4×#22576775, … |
| maximal normal subgroup of | C4×D4×D547, C2×(C22⋊D547)⋊C4, C4×#22576775, … |
| maximal quotient of | #46854848, C22⋊C4×Dic547, #46854852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 106);