Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C541 ⋊ C4 |
| Sylow | C541 ⋊ #102 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^5,541|a^2=d,c^2=e,b^a=bc,c^a=ce,f^a=f^52,c^b=ce,f^d=f^540689 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#31772690, #46831165, #46831166, … |
| maximal normal subgroup of | C2×#31772690, #46831165, #46831166, … |
| maximal quotient of | D4⋊#16864520, #46831023, #46831026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 208);