Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6866 ⋊ C2 |
| derived | C32⋊C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4169 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6866 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
105 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 18 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2)(3,14,11,8,9,16)(4,12)(5,7)(6,13)(10,15)(17,18);(1,11,13,5,9,10,4,3,17)(2,18,8,12,15,14,7,6,16)Polycyclic presentation:
2,3^5|c^3=e^2,c^a=c^2e,d^a=d^2f,e^a=e^2,c^b=cd,d^c=df39 conjugacy classes — view the full character table.
| maximal subgroup of | #92173⋊C2, C2×#92174, #13090501, … |
| maximal normal subgroup of | #92173⋊C2, C2×#92174, C3×#92174, … |
| maximal quotient of | #11757297, C2×#92174, #13090436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 19);