Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C541 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^5404334 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46829911, #46829913, #46830326, … |
| maximal normal subgroup of | #46829911, #46829913, #46830326, … |
| maximal quotient of | #46830035, #46830048, #46830059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 125);