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×#60129 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C24×C4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ G | |
2038 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,24,28,25,29,35,41)(22,26,32,38,30,36,43,47)(23,27,34,40,33,39,45,49)(31,37,44,48,42,46,50,51);(13,16)(17,19)(20,22)(21,26)(23,31)(24,32)(25,30)(27,37)(28,38)(29,36)(33,42)(34,44)(35,43)(39,46)(40,48)(41,47)(45,50)(49,51);(12,14,15,18)(13,17,16,19)(22,30)(26,36)(31,42)(32,43)(37,46)(38,47)(44,50)(48,51);(20,23)(21,27)(22,31)(24,34)(25,33)(26,37)(28,40)(29,39)(30,42)(32,44)(35,45)(36,46)(38,48)(41,49)(43,50)(47,51);(23,33)(27,39)(31,42)(34,45)(37,46)(40,49)(44,50)(48,51)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53117);