Finite Group DatabasebetaFinite Group Databasebeta| order | 486 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C3 |
| direct product | C2×#6899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C33 |
| commutator, Frattini, cosocle | C32 | C2×C33 |
| prime radical | C2×C33 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ G | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 162 |
A minimal faithful permutation representation — 3 generators on 38 points:
(1,2)(4,5,9)(7,10,8)(12,13,17)(14,21,31)(15,20,25)(16,18,27)(19,28,23)(22,33,37)(24,30,26)(29,38,35)(32,36,34);(3,4,7,11,9,10,6,5,8)(13,18,20)(17,25,27)(19,21,30)(26,31,28)(29,32,33)(36,38,37);(3,5,10,11,4,8,6,9,7)(12,14,22,16,24,35,15,23,34)(13,19,29,18,21,32,20,30,33)(17,26,36,27,28,37,25,31,38)102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(486, 205);