Finite Group DatabasebetaFinite Group Databasebeta| order | 4599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#13095275 |
| Fitting, socle | C3×C7×C73 ⋊ C3 |
| derived, Hall | C7×C73 ⋊ C32 |
| Sylow | C73 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13095275 |
| commutator, cosocle, hypocenter | C7×C73 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C73 | C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1533 |
519 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×#13095275, C3×C22⋊#13095275, C3×C5×#13095275, … |
| maximal normal subgroup of | C3×C5×#13095275, C3×C7×#13095275 |
| maximal quotient of | A4×#13095275, C3×C22⋊#13095275, C3×C5×#13095275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4599, 11);