Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #6908 ⋊ C2 |
| derived | C32×C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C9 | C2×C3 |
| Frattini | C32 | C3×C3⋊D3 |
| Fitting | #6908 | C2 |
| socle | C3 | C3⋊((C3⋊D3)⋊C3) |
| LCS | G ▷ C32×C9 | |
| UCS | C1 | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,5)(3,16,13,9,7,22)(4,8,14,12,6,19)(10,15,23,11,17,24)(18,27,21,25,26,20);(1,21,9,12,11,10,4,3,20)(2,18,16,8,15,17,6,7,25)(5,26,22,19,24,23,14,13,27);(2,6,8)(7,15,18)(16,25,17)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,e^b=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | #92280⋊C2, C2×#92330, #10624526⋊C2, … |
| maximal normal subgroup of | #92280⋊C2, C2×#92330, C3×#92330, … |
| maximal quotient of | #11757634, C2×#92330, #13090710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 175);