Finite Group DatabasebetaFinite Group Databasebeta| order | 588 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C49 |
| unambiguous semidirect product | C3⋊(C4×C49) |
| derived, Sylow | C3 ⋊ C4×C49 |
| Hall | C3×C49 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D3 |
| commutator, hypocenter | C3 | C4×C49 |
| Frattini | C2×C7 | D3×C7 |
| Fitting | C2×C3×C49 | C2 |
| socle, prime radical, cosocle | C2×C3×C7 | C2×C7 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C49 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 588 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #11924097, Dic3×D49, D147⋊C4, … |
| maximal normal subgroup of | #11924097, Dic3×D49, D147⋊C4, … |
| maximal quotient of | C3⋊C8×C49, C2×Dic3×C49, Dic9×C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(588, 3);