Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#36700 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| socle | C23×C11 | C25 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
1356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
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)(15,19)(16,18)(20,21)(22,26)(23,27)(24,25)(28,31)(29,33)(30,32)(34,35)(36,37,40,43)(38,41,45,49)(39,42,47,51)(44,48,46,50);(12,14,16,15)(13,17,18,19)(21,25)(26,31)(27,32)(33,35)(36,38,40,45)(37,41,43,49)(39,46,47,44)(42,50,51,48);(13,18)(17,19)(20,22)(21,26)(23,29)(24,28)(25,31)(27,33)(30,34)(32,35)(36,39)(37,42)(38,44)(40,47)(41,48)(43,51)(45,46)(49,50);(12,15,16,14)(13,19,18,17)(22,28)(26,31)(29,34)(33,35)(37,43)(39,47)(41,49)(44,46);(20,23,24,30)(21,27,25,32)(22,29,28,34)(26,33,31,35)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 29688);