Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C541 ⋊ #131 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|a^2=d,d^2=e,f^a=f^52,c^b=ce,f^b=f^540,f^c=f^540,f^d=f^540695 conjugacy classes — view the full character table.
| maximal subgroup of | #46831218, #46831219, #46831220, … |
| maximal normal subgroup of | #46831218, #46831219, #46831220, … |
| maximal quotient of | #46831140, #46831150, #46831182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 234);