Finite Group DatabasebetaFinite Group Databasebeta| order | 1204 |
| isoclinism | isoclinic class of D43⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic43⋊C7 |
| unambiguous semidirect product | (C43⋊C7)⋊C4 |
| derived, Sylow | C43 ⋊ C4×C7 |
| Hall | C43⋊C7 ⋊ C4 |
| Hall | Dic43 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D43⋊C7 |
| commutator, hypocenter | C43 | C4×C7 |
| Fitting, socle, cosocle | C2×C43 | C2×C7 |
| prime radical | C2×C43⋊C7 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 172 |
Polycyclic presentation:
2,7,2,43|a^2=c,d^a=d^42,d^b=d^3534 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1204, 1);