Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C541 ⋊ C2 |
| Sylow | C541 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^5,541|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^540,d^b=de,f^b=f^5402711 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46830344, #46830345, #46830349, … |
| maximal normal subgroup of | #46830344, #46830345, #46830349, … |
| maximal quotient of | #46830177, #46830181, #46830217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 174);