Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | C32⋊H(3,𝔽3) ⋊ C2 |
| derived | C33 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33 | C2×C32 |
| Frattini, socle | C32 | C32×D3 |
| Fitting | C32⋊H(3,𝔽3) | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 | |
171 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 2 generators on 18 points:
(2,4)(3,6)(5,7)(8,9)(11,16,18,13,14,17)(12,15);(1,2,8)(3,5,7)(4,6,9)(10,11,13)(12,14,17)(15,18,16)Polycyclic presentation:
2,3^5|d^a=d^2,e^a=e^2,f^a=f^2,d^b=de,d^c=df39 conjugacy classes — view the full character table.
| maximal subgroup of | (((C3⋊D3)⋊C3)⋊D3)⋊C3, #11757731, C2×#92258, … |
| maximal normal subgroup of | (((C3⋊D3)⋊C3)⋊D3)⋊C3, #11757731, C2×#92258, … |
| maximal quotient of | #11757562, C2×#92258, #13090619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 103);