Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6878 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11 · Schur multiplier (H2) = C3×C9 |
| direct product | C11×#6879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C11 | #732 |
| commutator, Frattini, cosocle | C3×C9 | C32×C11 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C11 ◁ C32×C11 ◁ C3×C9×C11 ◁ G | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 297 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16)(14,18,23)(15,19,26)(17,27,32)(20,30,34)(21,28,24)(22,31,25)(29,36,38)(33,37,35);(13,17,28,19,29,37,31,30,18)(16,23,34,25,35,36,26,24,27)385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 26);