Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34530 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,22)(19,26)(20,21)(23,27)(24,30)(25,28)(29,31)(32,33,37,40)(34,35,42,38)(36,44,45,39)(41,46,47,43);(17,21)(22,28)(23,26)(29,30)(32,34,37,42)(33,38,40,35)(36,41,45,47)(39,46,44,43);(12,13,15,14)(16,18,20,25)(17,22,21,28)(19,24,27,31)(23,29,26,30)(32,34)(33,38)(35,40)(36,41)(37,42)(39,46)(43,44)(45,47);(16,17)(18,22)(19,23)(20,21)(24,29)(25,28)(26,27)(30,31)(32,35,37,38)(33,34,40,42)(36,43,45,46)(39,41,44,47);(12,14,15,13)(16,19)(17,23)(18,24)(20,27)(21,26)(22,29)(25,31)(28,30)(32,36,37,45)(33,39,40,44)(34,41,42,47)(35,43,38,46)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27518);