Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C541 ⋊ #108 |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^52,f^b=f^540,f^d=f^5401094 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46831089, #46831090, #46831103, … |
| maximal normal subgroup of | #46831089, #46831090, #46831103, … |
| maximal quotient of | #46831037, #46831038, #46831051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 217);