Finite Group DatabasebetaFinite Group Databasebeta| order | 13712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C857 ⋊ C2 |
| Sylow | C857 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6856 |
Polycyclic presentation:
2^4,857|a^2=d,b^a=bc,e^b=e^8563434 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D857, C2×#28351406, #42116786, … |
| maximal normal subgroup of | C22⋊C4×D857, C2×#28351406, #42116786, … |
| maximal quotient of | #42116736, #42116741, #42116743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13712, 17);