Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60557 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ 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)(22,27)(23,35)(24,29)(25,38)(26,30)(28,36)(31,45)(32,41)(33,42)(34,48)(37,43)(39,44)(40,47)(46,51)(49,50);(13,16)(17,19)(20,22)(21,27)(23,31)(24,33)(25,34)(26,32)(28,40)(29,42)(30,41)(35,45)(36,47)(37,46)(38,48)(39,49)(43,51)(44,50);(20,23)(21,28)(22,31)(24,36)(25,39)(26,37)(27,40)(29,43)(30,44)(32,46)(33,47)(34,49)(35,38)(41,50)(42,51)(45,48);(12,14,15,18)(13,17,16,19)(22,32)(27,41)(31,46)(33,34)(40,50)(42,48)(45,51)(47,49);(20,24,26,25)(21,29,30,38)(22,33,32,34)(23,36,37,39)(27,42,41,48)(28,43,44,35)(31,47,46,49)(40,51,50,45)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53545);