Finite Group DatabasebetaFinite Group Databasebeta| order | 588 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic21 |
| unambiguous semidirect product | C3⋊(C7×Dic7) |
| unambiguous semidirect product | C7⋊(C7×Dic3) |
| derived | C3×C7 ⋊ C4×C7 |
| Hall | C3×C72 ⋊ C4 |
| Sylow | C72 ⋊ Dic3 |
| Sylow | C3 ⋊ C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D21 |
| commutator, hypocenter | C3×C7 | C4×C7 |
| Frattini | C2 | C7×D21 |
| Fitting, socle, prime radical | C2×C3×C72 | C2 |
| cosocle | C2×C3×C7 | C2×C7 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C7×Dic3×D7, D3×C7×Dic7, C7×#4245, … |
| maximal normal subgroup of | C7×Dic3×D7, D3×C7×Dic7, C7×#4245, … |
| maximal quotient of | C7×C3⋊(C7⋊C8), C2×C7×Dic21, C7×Dic63, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(588, 30);