Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23425 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
1938 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(20,21,26,31)(22,32,34,43)(23,37,40,44)(24,30,25,29)(27,36,42,35)(28,38,45,39)(33,47,48,41)(46,49,51,50);(13,15)(16,17)(18,19)(20,22)(21,27)(23,33)(24,36)(25,35)(26,34)(28,41)(29,43)(30,32)(31,42)(37,51)(38,50)(39,49)(40,48)(44,46)(45,47);(17,19)(20,23,26,40)(21,28,31,45)(22,33,34,48)(24,39,25,38)(27,41,42,47)(29,37,30,44)(32,46,43,51)(35,50,36,49);(22,34)(27,42)(32,43)(33,48)(35,36)(41,47)(46,51)(49,50)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16413);