Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92182 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6872 ⋊ 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 | #6872 | 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)(8,25,59,9,27,51)(10,57,52,31,26,48)(13,68,67,38,37,65)(15,42)(16,43)(19,32,46,24,21,58)(20,71,72,40,45,79)(23,60,50,53,28,75)(29,80,77,62,55,74)(30,76,78,61,56,54)(34,39,66,41,64,69)(47,63,73,70,49,81);(1,40,31,43,30,28,4,2,62,17,63,21,15,9,8,42,32,49,5,29,6,14,60,61,16,10,20)(3,71,44,69,56,54,13,7,72,36,81,48,39,25,23,67,58,74,12,55,19,41,75,59,37,26,47)(11,70,57,68,51,50,34,24,80,33,77,46,65,53,27,64,52,73,35,79,18,38,78,76,66,22,45)Polycyclic presentation:
2,3^5|c^3=e^2f^2,e^3=f,c^a=c^2e,d^a=d^2,e^a=e^2f^2,f^a=f^2,c^b=cd,d^b=df30 conjugacy classes — view the full character table.
| maximal subgroup of | #92181⋊C2, C2×#92182, C3×#92182, … |
| maximal normal subgroup of | #92181⋊C2, C2×#92182, C3×#92182, … |
| maximal quotient of | #11757305, C2×#92182, #13090446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 27);