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×#6896 |
| 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 | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 891 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17,19)(14,18,20)(22,23,27)(25,28,26);(12,13,18,16,19,20,15,17,14)(21,22,25,24,23,26,29,27,28);(12,14,17,15,20,19,16,18,13)(21,23,28,24,27,25,29,22,26)561 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 43);