Finite Group DatabasebetaFinite Group Databasebeta| order | 2044 |
| isoclinism | isoclinic class of D7×D73 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D73 |
| unambiguous semidirect product | (D7×C73)⋊C2 |
| unambiguous semidirect product | (C7×D73)⋊C2 |
| unambiguous semidirect product | D511⋊C2 |
| Fitting, socle, derived, Hall | C7×C73 ⋊ C22 |
| Sylow | C73 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C73 | C22 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 511 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | D49×D73, C7×D7×D73, C7⋊D7×D73, … |
| maximal normal subgroup of | C7×D7×D73, C11×D7×D73, C13×D7×D73, … |
| maximal quotient of | D49×D73, C7×D7×D73, C7⋊D7×D73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2044, 8);