Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92191 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6879 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #732 | C2×C3 |
| Frattini | C3×C9 | C3×D3 |
| Fitting | #6879 | C2 |
| socle | C3 | #4178 |
| LCS | G ▷ #732 | |
| UCS | C1 | |
33 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 2 generators on 27 points:
(2,24,21,15,19,14,8,13,27,5,18,17,7,26,16,20,6,25)(3,9)(4,12)(10,11)(22,23);(1,2,5)(3,6,17)(4,8,15)(7,20,12)(9,21,13)(10,16,26)(11,19,14)(18,25,23)(22,27,24)Polycyclic presentation:
2,3^5|b^3=e,d^3=f^2,c^a=c^2,d^a=d^2ef,f^a=f^2,c^b=cd,d^c=def,e^c=ef31 conjugacy classes — view the full character table.
| maximal subgroup of | #92191⋊C2, C2×#92191, #13090586, … |
| maximal normal subgroup of | #92191⋊C2, C2×#92191, C3×#92191, … |
| maximal quotient of | #11757314, C2×#92191, #13090510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 36);