Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊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^b=f^546,f^c=f^5462750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46855081, #46855083, #46855086, … |
| maximal normal subgroup of | #46855081, #46855083, #46855086, … |
| maximal quotient of | #46854848, C4⋊C4×Dic547, #46854872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 108);