Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#34192 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
2250 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,20)(21,23)(25,28)(26,32)(31,35)(33,38);(24,25,29,28)(26,30,32,34)(27,35,36,31)(33,39,38,37);(16,17)(18,21)(19,20)(22,23)(24,26)(25,30)(27,33)(28,34)(29,32)(31,37)(35,39)(36,38);(24,27,29,36)(25,31,28,35)(26,33,32,38)(30,37,34,39);(16,18,19,22)(17,21,20,23)(24,28,29,25)(26,34,32,30)(27,35,36,31)(33,39,38,37)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27180);