Finite Group DatabasebetaFinite Group Databasebeta| order | 30366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C241 · Schur multiplier (H2) = C1 |
| direct product | C3⋊AGL(1,𝔽7)×C241 |
| unambiguous semidirect product | C3⋊(AGL(1,𝔽7)×C241) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(D3×C241) |
| unambiguous semidirect product | D21⋊(C3×C241) |
| Fitting, socle | C3×C7×C241 ⋊ C2×C3 |
| derived | C3×C7 ⋊ C2×C3×C241 |
| Hall | C3×ΓL(1,𝔽8)×C241 ⋊ C2 |
| Hall | C7×C241 ⋊ C3×D3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×C241 |
| Sylow | C7 ⋊ C3×D3×C241 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C241 | C3⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C3×C7 | C2×C3×C241 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C241 | C2×C3 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C241 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5061 |
2892 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30366, 44);