Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6893 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C3 |
| Frattini, socle | C32 | C3×C3⋊D3 |
| Fitting | #6893 | C2 |
| prime radical | C3⋊#272 | C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 54 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,7,9,4,5,8)(3,6)(10,16,32,13,26,14,20,11,22)(12,33,30,27,24,29,18,23,31,17,25,36,19,34,21,28,15,35);(12,18,19)(15,24,25)(17,27,28)(21,30,31)(23,33,34)(29,35,36);(1,2,4)(3,5,8)(6,9,7)(10,12,17)(11,15,23)(13,19,27)(14,21,29)(16,25,33)(18,28,20)(22,31,35)(24,34,26)(30,36,32)Polycyclic presentation:
2,3^5|b^3=f,c^a=c^2,d^a=d^2,e^a=e^2,c^b=ce,d^c=df39 conjugacy classes — view the full character table.
| maximal subgroup of | #92304⋊C2, C2×#92305, #10624627⋊C2, … |
| maximal normal subgroup of | #92304⋊C2, C2×#92305, #10624627⋊C2, … |
| maximal quotient of | #11757609, C2×#92305, #13090627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 150);