Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92192 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting, Sylow | #6879 ⋊ C2 |
| derived | C92 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C92 | C2×C3 |
| Frattini | C3×C9 | C3×D3 |
| Fitting | #6879 | C2 |
| socle | C3 | #4179 |
| LCS | G ▷ C92 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,5)(3,6,14,10,7,17)(4,8,16,13,9,22)(11,18,25,12,19,15)(20,27,23,21,26,24);(2,20,7,9,19,18,8,6,21)(5,27,17,22,15,25,16,14,26)Polycyclic presentation:
2,3^5|c^3=e^2,d^3=f^2,c^a=c^2e,d^a=d^2f,e^a=e^2,f^a=f^2,c^b=cd,d^b=def,e^b=ef22 conjugacy classes — view the full character table.
| maximal subgroup of | #92191⋊C2, C2×#92192, #13090584, … |
| maximal normal subgroup of | #92191⋊C2, C2×#92192, C3×#92192, … |
| maximal quotient of | #11757315, C2×#92192, #13090509, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 37);