Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C541 ⋊ C2 |
| Sylow | C541 ⋊ #123 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|c^2=d,b^a=bd,c^a=ce,f^b=f^5402714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D541, C2×#31772610, #46830684, … |
| maximal normal subgroup of | #123×D541, C2×#31772610, #46830684, … |
| maximal quotient of | #46830037, #46830049, #46830051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 128);