Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #4179 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6868 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4179 |
| commutator, hypocenter | C3×C9 | C2×C9 |
| Frattini | C33 | C3×D3 |
| Fitting | #6868 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| prime radical | C3×C3⋊D9 | C3 |
| cosocle | C32×C9 | C2×C3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C3 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,5,9,3,8,4,6,2,7)(11,21,24,14,15,25)(12,30,32,18,19,31)(13,20)(16,27,34,17,28,35)(22,29,33,26,23,36);(10,29,14,20,17,16,13,11,23)(12,36,22,32,27,25,19,15,34)(18,35,21,30,24,28,31,26,33)Polycyclic presentation:
2,3^5|b^3=c,d^3=f^2,d^a=d^2f,e^a=e^2,f^a=f^2,d^b=de,e^b=ef39 conjugacy classes — view the full character table.
| maximal subgroup of | #92177⋊C2, C2×#92177, #13090509, … |
| maximal normal subgroup of | #92177⋊C2, C2×#92177, C3×#92177, … |
| maximal quotient of | #11757300, C2×#92177, #13090441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 22);