Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92303 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | C9⋊H(3,𝔽3) ⋊ C2 |
| derived | C32×C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | C9⋊H(3,𝔽3) | C2 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
109 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,7,9,4,5,8)(3,6)(11,15,18,13,14,17)(12,16);(10,18,13,16,14,15,12,11,17);(1,2,4)(3,5,8)(6,9,7)Polycyclic presentation:
2,3^5|d^3=f^2,c^a=c^2,d^a=d^2f,e^a=e^2,f^a=f^2,c^b=ce,d^b=df30 conjugacy classes — view the full character table.
| maximal subgroup of | D9⋊((C3⋊D3)⋊C3), C2×#92303, #13091213, … |
| maximal normal subgroup of | D9⋊((C3⋊D3)⋊C3), C2×#92303, C3×#92303, … |
| maximal quotient of | #11757607, C2×#92303, #13090624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 148);