Finite Group DatabasebetaFinite Group Databasebeta| order | 1744 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#11724784 |
| derived, Sylow | C109 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D109 |
| commutator, hypocenter | C109 | C2×C8 |
| Frattini | C4 | C2×D109 |
| Fitting | C2×C4×C109 | C2 |
| socle, prime radical | C22×C109 | C4 |
| cosocle | C4×C109 | C22 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1744 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic109, C4×#11724784, #16812609, … |
| maximal normal subgroup of | C8×Dic109, C4×#11724784, #16812609, … |
| maximal quotient of | C4×#11724784, C22⋊#11724784, C4⋊#11724784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1744, 22);