Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#21003 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×#121 |
| prime radical | C2×C11×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
1686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,21,27,22,26,20,25)(18,23,29,37,30,39,31,38)(19,32,33,24,34,40,35,41)(28,42,44,36,45,46,43,47);(16,18,21,31,22,30,20,29)(17,23,25,37,26,39,27,38)(19,28,35,44,34,45,33,43)(24,36,40,42,41,47,32,46);(13,15)(16,19)(17,24)(18,28)(20,33)(21,35)(22,34)(23,36)(25,40)(26,41)(27,32)(29,43)(30,45)(31,44)(37,42)(38,46)(39,47);(16,20,22,21)(17,25,26,27)(18,29,30,31)(19,33,34,35)(23,37,39,38)(24,40,41,32)(28,43,45,44)(36,42,47,46)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13991);