Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92203 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #6861 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6861 | C2 |
| Frattini | C33 | C3⋊D3 |
| socle | C32 | #272 |
| LCS | G ▷ #6861 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 54 points:
(2,5)(3,9)(4,13)(6,8)(7,17)(10,12)(11,21)(14,24)(15,20)(16,22)(18,26)(19,25)(23,27)(29,33)(30,38)(31,32)(34,36)(35,46)(37,44)(39,51)(40,42)(41,50)(43,53)(45,52)(47,48)(49,54);(1,11,9,13,12,10,4,3,21)(2,23,24,20,19,18,8,7,22)(5,16,17,6,26,25,15,14,27)(28,41,38,32,42,40,31,30,50)(29,39,53,37,49,48,36,35,52)(33,45,46,34,47,54,44,43,51);(1,20,5,13,8,6,4,2,15)(3,23,26,11,19,14,12,7,16)(9,22,17,10,24,25,21,18,27)(28,37,33,32,36,34,31,29,44)(30,49,47,41,35,43,42,39,45)(38,52,51,40,53,46,50,48,54)Polycyclic presentation:
2,3^5|b^3=e^2,c^3=e^2,b^a=b^2e,c^a=c^2e,d^a=de^2f,e^a=e^2,f^a=f^2,c^b=cd,d^b=def,d^c=df22 conjugacy classes — view the full character table.
| maximal subgroup of | #92165⋊C2, C2×#92203, C3×#92203, … |
| maximal normal subgroup of | #92165⋊C2, C2×#92203, C3×#92203, … |
| maximal quotient of | #11757326, C2×#92203, #13090453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 48);