Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92180 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | H(3,𝔽3)⋊C9 ⋊ C2 |
| derived | C32×C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | H(3,𝔽3)⋊C9 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,4)(3,6,8,7,5,9)(11,13)(12,16)(14,15)(17,18);(2,5,6)(10,18,13,16,15,14,12,11,17)Polycyclic presentation:
2,3^5|c^3=f^2,c^a=c^2f,d^a=d^2,e^a=e^2,f^a=f^2,c^b=cd,d^b=de30 conjugacy classes — view the full character table.
| maximal subgroup of | (#272⋊C9)⋊C2, C2×#92180, C3×#92180, … |
| maximal normal subgroup of | (#272⋊C9)⋊C2, C2×#92180, C3×#92180, … |
| maximal quotient of | #11757303, C2×#92180, #13090446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 25);