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×#6909 |
| 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 ◁ C33×C11 ◁ G | |
148 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)(14,20,25)(15,19,26)(17,27,23)(18,30,24)(21,32,35)(22,29,36)(28,38,34)(31,37,33);(12,14,21)(13,17,28)(15,23,33)(16,25,35)(18,20,31)(19,29,32)(22,34,24)(26,27,37)(30,36,38);(14,22,23)(17,20,29)(21,33,34)(25,36,27)(28,32,31)(35,37,38)385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 56);