Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92161 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6862 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4177 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6862 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | #4181 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
35 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 54 points:
(1,30,39,11,14,27,6,8,40,2,15,31,7,9,12,26,3,53)(4,50,22,32,5,41,19,36,43,16,25,47,20,21,13,28,17,54)(10,38,49,24,29,18,51,42,52,34,33,23,37,48,45,44,35,46);(1,19,14,6,20,15,7,4,3)(2,8,16,11,30,32,26,9,28)(5,46,13,25,18,22,17,23,43)(10,33,53,37,29,31,51,35,27)(12,42,44,39,48,24,40,38,34)(21,54,49,36,47,45,50,41,52)Polycyclic presentation:
2,3^5|b^3=f,c^3=e,c^a=c^2e^2,d^a=d^2f^2,e^a=e^2,c^b=cd,d^b=de,d^c=df^231 conjugacy classes — view the full character table.
| maximal subgroup of | #92167⋊C2, C2×#92167, C3⋊#92167, … |
| maximal normal subgroup of | #92167⋊C2, C2×#92167, C3×#92167, … |
| maximal quotient of | #11757290, C2×#92167, #13090451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 12);