Finite Group DatabasebetaFinite Group Databasebeta| order | 3483 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C43 · Schur multiplier (H2) = C3 |
| direct product | C43×C9⋊C9 |
| unambiguous semidirect product | C9⋊(C9×C43) |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C32×C43 | C32 |
| commutator | C3 | C3×C9×C43 |
| Frattini, cosocle | C32 | C32×C43 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C43 ◁ G | |
34 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 3483 |
A minimal faithful permutation representation — 2 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43)(45,47,50)(48,52,51)(53,54,56,55,57,59,58,60,61);(44,45,48,46,47,51,49,50,52)1419 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3483, 4);