Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | #6893 ⋊ C2 |
| derived | C32⋊C9 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4207 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | #6893 | C2 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
99 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,4)(5,9)(6,8)(11,14)(12,28,30,18,19,29)(13,20)(15,17)(16,33,35,24,25,34)(21,36,23,26,31,32)(22,27);(2,5,6)(4,8,9)(10,12,18)(11,16,26)(13,19,29)(14,21,24)(15,23,33)(17,25,32)(20,30,28)(22,31,34)(27,35,36);(1,2,4)(3,6,8)(5,9,7)(10,27,14,20,17,15,13,11,22)(12,35,21,30,25,23,19,16,31)(18,36,24,28,32,33,29,26,34)Polycyclic presentation:
2,3^5|c^3=e^2,c^a=c^2e,d^a=d^2,e^a=e^2,d^b=de,d^c=df39 conjugacy classes — view the full character table.
| maximal subgroup of | #92304⋊C2, C2×#92304, #13091059, … |
| maximal normal subgroup of | #92304⋊C2, C2×#92304, C3×#92304, … |
| maximal quotient of | #11757608, C2×#92304, #13090626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 149);