Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C11 · Schur multiplier (H2) = C9 |
| direct product | C11×#6898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C11 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C11 |
| prime radical | C33×C11 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C11 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 891 |
A minimal faithful permutation representation — 3 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16)(14,18,24)(15,19,23)(17,25,22)(20,27,32)(21,28,31)(26,33,30)(29,35,37)(34,38,36)(39,40,43)(41,44,50)(42,46,51)(45,55,49)(47,52,58)(48,54,59)(53,62,57)(56,61,64)(60,65,63);(13,17,19)(16,23,25)(18,26,28)(24,31,33)(27,34,35)(32,37,38)(39,41,47,42,48,56,49,57,63)(40,44,52,46,54,61,45,53,60)(43,50,58,51,59,64,55,62,65);(12,14,20,22,30,36,15,21,29)(13,18,27,17,26,34,19,28,35)(16,24,32,25,33,38,23,31,37)(40,45,46)(43,51,55)(44,53,54)(50,59,62)(52,60,61)(58,64,65)561 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 45);