Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92333 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | #6911 ⋊ C2 |
| derived | #732 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #732 | C2×C3 |
| Frattini | C32 | C3×C3⋊D3 |
| Fitting | #6911 | C2 |
| socle | C3 | C3×#272 |
| LCS | G ▷ #732 | |
| UCS | C1 | |
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 3 generators on 27 points:
(2,12,8,5,6,14)(3,9)(4,11)(7,25,19,16,15,26)(10,21)(13,20,24,18,17,27)(22,23);(1,3,9)(2,7,18)(4,10,22)(5,13,16)(6,15,20)(8,19,27)(11,23,21)(12,17,25)(14,24,26);(1,2,5)(3,7,17)(4,6,14)(8,12,11)(9,20,16)(10,15,13)(18,25,21)(19,24,23)(22,27,26)Polycyclic presentation:
2,3^5|c^a=c^2,d^a=d^2,f^a=f^2,c^b=cf,d^c=de,e^c=ef,e^d=ef^231 conjugacy classes — view the full character table.
| maximal subgroup of | (#4178⋊C2)⋊C3, C2×#92333, #13091107, … |
| maximal normal subgroup of | (#4178⋊C2)⋊C3, C2×#92333, #92191⋊C3, … |
| maximal quotient of | #11757637, C2×#92333, #13090734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 178);