Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| isoclinism | isoclinic class of #92391 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | H(5,𝔽3) ⋊ C2 |
| derived | C33 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33 | C2×C32 |
| Frattini, socle | C3 | C32×C3⋊D3 |
| Fitting | H(5,𝔽3) | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 | |
223 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
A minimal faithful permutation representation — 3 generators on 27 points:
(2,11,14,5,6,13)(3,8)(4,10)(7,24,23,16,15,26)(9,18)(12,25,22,17,21,27)(19,20);(1,3,19)(2,7,25)(4,9,18)(5,12,26)(6,15,27)(8,10,20)(11,21,16)(13,22,24)(14,23,17);(1,2,5)(3,7,12)(4,6,13)(8,17,16)(9,15,22)(10,14,11)(18,27,24)(19,25,26)(20,23,21)Polycyclic presentation:
2,3^5|d^a=d^2,e^a=e^2,f^a=f^2,e^b=ef,d^c=df55 conjugacy classes — view the full character table.
| maximal subgroup of | #66432⋊C3, #11758086, C2×#92391, … |
| maximal normal subgroup of | #66432⋊C3, #11758086, C2×#92391, … |
| maximal quotient of | #11758012, C2×#92391, #13091379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 236);