Finite Group DatabasebetaFinite Group Databasebeta| order | 4599 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C7×C73 ⋊ C32 |
| Sylow | C73 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C73 | C32 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 511 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4599, 10);