Finite Group DatabasebetaFinite Group Databasebeta| order | 4338 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C241⋊C9 |
| unambiguous semidirect product | (C2×C241)⋊C9 |
| derived, Sylow | C241 ⋊ C2×C9 |
| Hall | C2×C241 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C241⋊C3 |
| commutator, hypocenter | C241 | C2×C9 |
| Frattini | C3 | C2×C241⋊C3 |
| Fitting, socle, prime radical | C2×C3×C241 | C3 |
| cosocle | C3×C241 | C2×C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 252 |
| transitive degree | μt(G) = 4338 |
498 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C241⋊C9, C2×(C241⋊C5)⋊C9, D5×C241⋊C9, … |
| maximal normal subgroup of | C2×C5×C241⋊C9, C2×(C241⋊C5)⋊C9, C2×C7×C241⋊C9 |
| maximal quotient of | C2×C5×C241⋊C9, D5×C241⋊C9, C2×C7×C241⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4338, 3);