Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6909 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C11 · Schur multiplier (H2) = C33 |
| direct product | C11×#6913 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C11 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C33×C11 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C11 ◁ C3×C9×C11 ◁ G | |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 297 |
A minimal faithful permutation representation — 3 generators on 38 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16)(14,18,23)(15,17,24)(19,28,22)(20,25,32)(21,27,33)(26,35,29)(30,34,37)(31,36,38);(13,17,19)(14,20,29)(18,26,25)(21,31,30)(23,32,35)(33,38,37);(12,14,21,15,20,30,22,29,31)(13,18,27,17,25,34,19,26,36)(16,23,33,24,32,37,28,35,38)385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 60);