Finite Group DatabasebetaFinite Group Databasebeta| order | 5744 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C359 · Schur multiplier (H2) = C1 |
| direct product | M16×C359 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C359 | C22 |
| commutator | C2 | C2×C4×C359 |
| Frattini, cosocle | C4 | C22×C359 |
| socle | C2×C359 | C2×C4 |
| prime radical | C22×C359 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C359 ◁ G | |
20 conjugacy classes of subgroups.
3590 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×C359, #101×C359, #104×C359, … |
| maximal normal subgroup of | #100×C359, #101×C359, #104×C359, … |
| maximal quotient of | #97×C359, C22⋊C8×C359, C4⋊C8×C359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5744, 6);