Finite Group DatabasebetaFinite Group Databasebeta| order | 903 |
| isoclinism | isoclinic class of (C43⋊C3)⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C3)⋊C7 |
| unambiguous semidirect product | (C43⋊C7)⋊C3 |
| Fitting, socle, derived, Sylow | C43 ⋊ C3×C7 |
| Hall | C43⋊C7 ⋊ C3 |
| Hall | C43⋊C3 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43 | C3×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 43 |
Polycyclic presentation:
3,7,43|c^a=c^36,c^b=c^4123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(903, 1);