Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60724 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
1874 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)(22,31)(23,34)(24,27)(25,29)(26,40)(28,37)(30,39)(32,46)(33,42)(35,48)(36,49)(38,45)(41,50)(43,51)(44,47);(13,16)(17,19)(20,22,25,24)(21,27,29,31)(23,32,36,35)(26,33,39,38)(28,41,43,44)(30,42,40,45)(34,48,49,46)(37,47,51,50);(20,23,26,37,25,36,39,51)(21,28,30,34,29,43,40,49)(22,32,33,47,24,35,38,50)(27,41,42,48,31,44,45,46);(12,14,15,18)(13,17,16,19)(20,24,25,22)(21,27,29,31)(23,35,36,32)(26,38,39,33)(28,41,43,44)(30,42,40,45)(34,48,49,46)(37,50,51,47);(22,24)(23,36)(27,31)(28,43)(33,38)(34,49)(37,51)(42,45)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53712);