Finite Group DatabasebetaFinite Group Databasebeta| order | 1744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C109 ⋊ M16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 872 |
Polycyclic presentation:
2^4,109|a^2=c,c^2=d,b^a=bd,e^a=e^108442 conjugacy classes — view the full character table.
| maximal subgroup of | #16812615, #16812616, #16812617, … |
| maximal normal subgroup of | #16812615, #16812616, #16812617, … |
| maximal quotient of | #16812610, C22⋊#11724784, C4⋊#11724784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1744, 24);