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×#34387 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(17,21)(18,24)(23,28)(25,30)(32,33)(34,37)(35,40)(36,41)(38,42)(39,44)(43,45)(46,47);(17,21)(22,27)(23,28)(29,31)(33,34)(35,42)(39,41)(43,47);(16,17)(18,22)(19,23)(20,21)(24,27)(25,29)(26,28)(30,31)(32,34,37,33)(35,40,42,38)(36,41,44,39)(43,46,47,45);(16,18)(17,22)(19,25)(20,24)(21,27)(23,29)(26,30)(28,31)(32,35)(33,38)(34,40)(36,43)(37,42)(39,45)(41,46)(44,47);(16,19,20,26)(17,23,21,28)(18,25,24,30)(22,29,27,31)(32,36,37,44)(33,39,34,41)(35,43,42,47)(38,45,40,46)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27375);