Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6867 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4169 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6867 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | #4181 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
51 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 36 points:
(2,4)(3,7)(5,6)(8,9)(10,16,33,13,27,14,21,11,23)(12,24,22,29,26,36,19,28,25,17,15,32,20,35,30,31,18,34);(1,9,4,7,6,5,3,2,8)(10,12,17)(11,15,24)(13,20,29)(14,22,32)(16,26,35)(18,28,27)(19,31,21)(23,30,36)(25,34,33)Polycyclic presentation:
2,3^5|b^3=f,c^3=e^2,c^a=c^2e,d^a=d^2f^2,e^a=e^2,c^b=cd,d^c=df^239 conjugacy classes — view the full character table.
| maximal subgroup of | #92175⋊C2, C2×#92176, #13090506, … |
| maximal normal subgroup of | #92175⋊C2, C2×#92176, C3×#92176, … |
| maximal quotient of | #11757299, C2×#92176, #13090439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 21);