Finite Group DatabasebetaFinite Group Databasebeta| order | 3773 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C11 · Schur multiplier (H2) = C72 |
| direct product | C11×H(3,𝔽7) |
| unambiguous semidirect product | C72⋊(C7×C11) |
| unambiguous semidirect product | (C72×C11)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C7×C11 | C72 |
| commutator, Frattini, cosocle | C7 | C72×C11 |
| LCS | G ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C7×C11 ◁ G | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 539 |
A minimal faithful permutation representation — 2 generators on 60 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,19,26,37,46)(14,17,21,28,39,48,55)(16,22,32,44,53,60,54)(18,24,31,41,50,47,56)(20,29,42,52,59,45,23)(25,35,30,43,38,49,57)(27,40,51,58,36,34,33);(13,16,23,34,35,24,17)(15,20,30,21,22,33,31)(19,27,28,29,41,32,43)(26,38,44,50,42,39,40)(37,47,51,53,48,49,52)(46,55,56,57,58,59,60)605 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3773, 3);