Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#11005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,21,25,22,27,20,26)(18,28,30,23,32,39,31,38)(19,33,35,24,36,41,34,42)(29,37,44,43,46,40,45,47);(16,18)(17,23)(19,29)(20,31)(21,30)(22,32)(24,40)(25,39)(26,28)(27,38)(33,43)(34,45)(35,44)(36,46)(37,42)(41,47);(13,15)(16,19,22,36)(17,24,27,42)(18,29,32,46)(20,35,21,34)(23,37,38,40)(25,33,26,41)(28,43,39,47)(30,45,31,44)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3993);