Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24311 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
1012 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,20,23)(18,22,19,21)(24,25)(26,36)(27,31)(28,35)(29,34)(30,33)(32,38)(37,39);(12,13)(14,15)(16,18,20,19)(17,21,23,22)(24,26,29,27)(25,31,34,36)(28,38,30,37)(32,35,39,33);(13,15)(24,27,29,26)(25,32,34,39)(28,38,30,37)(31,35,36,33);(16,19,20,18)(17,22,23,21)(24,28,29,30)(25,33,34,35)(26,37,27,38)(31,39,36,32)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17299);