Finite Group DatabasebetaFinite Group Databasebeta| order | 3483 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AΣL(1,𝔽27) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C43 · Schur multiplier (H2) = C3 |
| direct product | C43×#731 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C43 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C32×C43 |
| prime radical | H(3,𝔽3)×C43 | C3 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C43 ◁ C32×C43 ◁ G | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 70 |
| transitive degree | μt(G) = 1161 |
A minimal faithful permutation representation — 2 generators on 70 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)(44,45,48)(46,52,56)(47,51,57)(49,58,54)(50,61,55)(53,63,66)(59,69,70)(60,68,65)(62,67,64);(44,46,53,47,54,64,55,65,70)(45,49,59,51,60,63,50,52,62)(48,56,66,57,58,67,61,68,69)731 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3483, 8);