Finite Group DatabasebetaFinite Group Databasebeta| order | 1712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C107 ⋊ M16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 856 |
Polycyclic presentation:
2^4,107|a^2=c,c^2=d,b^a=bd,e^a=e^106434 conjugacy classes — view the full character table.
| maximal subgroup of | #16812025, #16812026, #16812027, … |
| maximal normal subgroup of | #16812025, #16812026, #16812027, … |
| maximal quotient of | #16812020, C22⋊(C107⋊C8), C4⋊(C107⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1712, 24);