Finite Group DatabasebetaFinite Group Databasebeta| order | 4599 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C73 ⋊ C9 |
| Sylow | C73 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ #10620321 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #13095275 |
| commutator, hypocenter | C7×C73 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C73 | C3 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 4599 |
Polycyclic presentation:
3,7,73,3|a^3=d,b^a=b^2,c^a=c^8519 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊#17987159, C5×#17987159, #44567123, … |
| maximal normal subgroup of | C5×#17987159, C7×#17987159 |
| maximal quotient of | C22⋊#17987159, C5×#17987159, #44567123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4599, 4);