Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C11 · Schur multiplier (H2) = C35 |
| direct product | C11×H(5,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C11 | C34 |
| commutator, Frattini, cosocle | C3 | C34×C11 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C11 ◁ G | |
586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 297 |
A minimal faithful permutation representation — 4 generators on 38 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16)(14,20,31)(15,19,26)(17,27,22)(18,30,24)(21,33,37)(23,29,25)(28,38,34)(32,36,35);(12,14,21)(13,17,28)(15,23,34)(16,25,36)(18,29,33)(19,20,32)(22,35,24)(26,27,37)(30,31,38);(14,22,23)(17,29,20)(21,34,35)(25,31,27)(28,32,33)(36,37,38);(13,18,19)(16,26,30)(17,29,20)(25,27,31)(28,33,32)(36,37,38)913 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 65);