Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6873 ⋊ 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 | #6873 | C2 |
| socle | C3 | #4169 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 2 generators on 81 points:
(2,18,22,6,7,44)(3,33,36,11,12,35)(4,14)(5,17)(8,25,60,9,27,52)(10,58,53,31,26,48)(13,64,66,38,37,68)(15,16)(19,32,46,24,21,59)(20,69,72,40,45,80)(23,61,51,54,28,76)(29,74,67,50,56,47)(30,73,77,49,57,55)(34,71,65,41,63,39)(42,43)(62,81,75,70,79,78);(1,40,21,42,61,49,4,2,50,5,70,31,15,9,8,16,10,62,17,29,6,14,30,28,43,32,20)(3,69,48,71,76,60,13,7,75,12,81,44,39,25,23,37,26,72,36,56,19,41,57,55,66,59,47)(11,67,46,68,77,73,34,24,74,35,80,58,64,54,27,65,22,79,33,78,18,38,52,51,63,53,45)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=cd,d^b=df30 conjugacy classes — view the full character table.
| maximal subgroup of | #92183⋊C2, C2×#92184, C3×#92184, … |
| maximal normal subgroup of | #92183⋊C2, C2×#92184, C3×#92184, … |
| maximal quotient of | #11757307, C2×#92184, #13090446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 29);