Finite Group DatabasebetaFinite Group Databasebeta| order | 1204 |
| isoclinism | isoclinic class of D7×D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D43 |
| unambiguous semidirect product | (D7×C43)⋊C2 |
| unambiguous semidirect product | (C7×D43)⋊C2 |
| unambiguous semidirect product | D301⋊C2 |
| Fitting, socle, derived, Hall | C7×C43 ⋊ C22 |
| Sylow | C43 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C43 | C22 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 301 |
115 conjugacy classes — view the full character table.
| maximal subgroup of | #14268588⋊C2, #14268587⋊C2, AGL(1,𝔽7)×D43, … |
| maximal normal subgroup of | #14268588⋊C2, #14268587⋊C2, AGL(1,𝔽7)×D43, … |
| maximal quotient of | C3×D7×D43, D21×D43, D7×D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1204, 9);