Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C3⋊(C3⋊D3))) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C310 |
| unambiguous semidirect product | C3⋊(C3⋊(C3⋊(C3⋊D3))) |
| Fitting, socle, derived, Sylow | C35 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C35 | C2 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
5328 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 243 |
A minimal faithful permutation representation — 6 generators on 15 points:
(2,3)(5,6)(8,9)(11,12)(14,15);(13,14,15);(10,11,12);(7,8,9);(4,5,6);(1,2,3)Polycyclic presentation:
2,3^5|b^a=b^2,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^2123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 260);