Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92172 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | C32⋊C27 ⋊ C2 |
| derived | C3×C27 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C27 | C2×C3 |
| Frattini | C3×C9 | C3×D3 |
| Fitting | C32⋊C27 | C2 |
| socle | C32 | C3×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 2 generators on 36 points:
(2,7,9,4,5,8)(3,6)(11,14)(12,18)(13,21)(15,16)(17,27)(19,20)(22,29)(23,28)(24,34)(25,33)(26,32)(30,31)(35,36);(1,2,4)(3,5,8)(6,9,7)(10,29,23,30,34,32,12,11,33,13,36,27,19,16,15,20,17,35,21,25,14,18,26,24,31,28,22)Polycyclic presentation:
2,3^5|c^3=e^2f,e^3=f^2,c^a=c^2e,d^a=d^2,e^a=e^2f,f^a=f^2,c^b=cd54 conjugacy classes — view the full character table.
| maximal subgroup of | ((C3⋊D3)⋊C27)⋊C2, C2×#92172, #13090437, … |
| maximal normal subgroup of | ((C3⋊D3)⋊C27)⋊C2, C2×#92172, C3×#92172, … |
| maximal quotient of | #11757295, C2×#92172, #13090436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 17);