Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting, Sylow | #6887 ⋊ C2 |
| derived | C92 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C92 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | #6887 | C2 |
| LCS | G ▷ C92 | |
| UCS | C1 | |
81 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,4)(3,7)(5,6)(8,9)(11,21,24,14,15,23)(12,17)(13,20)(16,32,34,26,25,35)(18,19)(22,36,33,28,31,27)(29,30);(10,30,17,20,19,18,13,12,29)(11,34,28,24,25,27,15,16,36)(14,31,26,21,33,32,23,22,35);(1,9,4,7,6,5,3,2,8)(10,11,14)(12,16,22)(13,15,23)(17,28,26)(18,27,32)(19,25,33)(20,24,21)(29,36,35)(30,34,31)Polycyclic presentation:
2,3^5|c^3=e^2,d^3=f^2,c^a=c^2e,d^a=d^2f,e^a=e^2,f^a=f^2,c^b=cf54 conjugacy classes — view the full character table.
| maximal subgroup of | #92294⋊C2, C2×#92296, #13090466, … |
| maximal normal subgroup of | #92294⋊C2, C2×#92296, #13090483, … |
| maximal quotient of | #11757600, C2×#92296, #13090605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 141);