Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | C32⋊H(3,𝔽3) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C32 | C3⋊(C3⋊D3) |
| commutator, Fitting, cosocle, hypocenter | C32⋊H(3,𝔽3) | C2 |
| LCS | G ▷ C32⋊H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
267 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 4 generators on 18 points:
(2,4)(5,9)(6,8)(11,13)(14,18)(15,17);(2,5,6)(4,8,9)(11,14,15)(13,17,18);(10,11,13)(12,15,17)(14,18,16);(1,2,4)(3,6,8)(5,9,7)Polycyclic presentation:
2,3^5|b^a=b^2,c^a=c^2,d^a=d^2,d^b=df,d^c=de39 conjugacy classes — view the full character table.
| maximal subgroup of | #11757730, #11757731, C2×#92338, … |
| maximal normal subgroup of | #11757730, #11757731, C2×#92338, … |
| maximal quotient of | #11757642, C2×#92338, #13090621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 183);