Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, derived, Sylow | #6908 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6908 | C2 |
| Frattini | C32 | C3⋊(C3⋊D3) |
| socle | C3 | C3⋊#272 |
| LCS | G ▷ #6908 | |
| UCS | C1 | |
119 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 4 generators on 27 points:
(2,6)(3,11)(4,5)(7,10)(8,17)(9,15)(12,22)(13,21)(14,18)(16,24)(19,26)(20,25)(23,27);(3,12,13)(8,19,20)(11,21,22)(14,16,23)(17,25,26)(18,27,24);(1,3,11)(2,8,18)(4,12,21)(5,13,22)(6,14,17)(7,16,25)(9,19,27)(10,20,24)(15,23,26);(1,9,6,4,10,7,5,2,15)(3,19,14,12,20,16,13,8,23)(11,27,17,21,24,25,22,18,26)Polycyclic presentation:
2,3^5|b^3=f^2,b^a=b^2f,c^a=c^2,d^a=d^2,e^a=ef^2,f^a=f^2,d^c=de,e^c=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | #92280⋊C2, C2×#92344, #13091020, … |
| maximal normal subgroup of | #92280⋊C2, C2×#92344, #13091296, … |
| maximal quotient of | #11757648, C2×#92344, #13090712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 189);