Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60682 |
| 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 | |
1878 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)(25,39)(26,30)(28,37)(31,44)(32,41)(33,42)(34,48)(36,43)(38,49)(40,47)(45,51)(46,50);(13,16)(17,19)(20,22)(21,27)(23,31)(24,33)(25,34)(26,32)(28,40)(29,42)(30,41)(35,44)(36,46)(37,47)(38,45)(39,48)(43,50)(49,51);(20,23,25,37,26,38,24,36)(21,28,29,35,30,43,39,49)(22,31,34,47,32,45,33,46)(27,40,42,44,41,50,48,51);(12,14,15,18)(13,17,16,19)(22,32)(27,41)(31,45)(33,34)(40,50)(42,48)(44,51)(46,47);(20,24,26,25)(21,29,30,39)(22,33,32,34)(23,36,38,37)(27,42,41,48)(28,35,43,49)(31,46,45,47)(40,44,50,51)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53670);