Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92199 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #6857 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #6857 | C2 |
| Frattini | C33 | C3⋊D3 |
| socle | C32 | #272 |
| LCS | G ▷ #6857 | |
| UCS | C1 | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 81 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,4)(3,7)(5,9)(6,8)(11,14)(12,17)(13,15)(16,18);(1,2,4)(3,6,9)(5,8,7)(10,14,17,13,18,16,15,12,11);(2,5,6)(4,8,9)(10,11,14)(12,15,16)(13,17,18)Polycyclic presentation:
2,3^5|c^3=e,b^a=b^2,c^a=c^2e^2,d^a=de^2f,e^a=e^2,f^a=f^2,c^b=cd,d^b=de,d^c=df^222 conjugacy classes — view the full character table.
| maximal subgroup of | #92161⋊C2, C2×#92199, C3×#92199, … |
| maximal normal subgroup of | #92161⋊C2, C2×#92199, C3×#92199, … |
| maximal quotient of | #11757322, C2×#92199, #13090450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 44);