Finite Group DatabasebetaFinite Group Databasebeta| order | 602 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D43 |
| Fitting, socle, Hall | C7×C43 ⋊ C2 |
| derived, Sylow | C43 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D43 |
| commutator, cosocle, hypocenter | C43 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C43 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 301 |
161 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D43, C2×C7×D43, C7×D43⋊C3, … |
| maximal normal subgroup of | D7×D43, C2×C7×D43, C7×D43⋊C3, … |
| maximal quotient of | C7×Dic43, C2×C7×D43, C3×C7×D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(602, 4);