Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #4177 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6867 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4177 |
| commutator, hypocenter | C3×C9 | C2×C9 |
| Frattini | C33 | C3×D3 |
| Fitting | #6867 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | C3×C3⋊D9 | C3 |
| cosocle | C32×C9 | C2×C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C3 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,5,9,3,8,4,6,2,7)(11,21,23,14,15,33)(12,30,32,18,19,31)(13,20)(16,36,22,27,28,25)(17,34,35,29,26,24);(10,17,14,13,27,16,20,11,29)(12,26,22,19,36,24,32,15,33)(18,23,21,31,35,28,30,25,34)Polycyclic presentation:
2,3^5|b^3=c,d^3=f,d^a=d^2f^2,e^a=e^2,f^a=f^2,d^b=de,e^b=ef39 conjugacy classes — view the full character table.
| maximal subgroup of | #92175⋊C2, C2×#92175, #13090504, … |
| maximal normal subgroup of | #92175⋊C2, C2×#92175, C3×#92175, … |
| maximal quotient of | #11757298, C2×#92175, #13090438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 20);