Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
970 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)(16,17,22,25,21,26,20,34)(18,27,36,38,29,44,30,23)(19,24,35,40,33,41,32,42)(28,43,46,37,45,39,31,47);(12,13)(14,15)(16,18,20,30,21,29,22,36)(17,23,25,27,26,38,34,44)(19,31,32,45,33,46,35,28)(24,39,40,47,41,43,42,37);(13,15)(16,19,21,33)(17,24,26,41)(18,28,29,45)(20,35,22,32)(23,37,38,47)(25,42,34,40)(27,43,44,39)(30,46,36,31);(18,29)(23,38)(27,44)(28,45)(30,36)(31,46)(37,47)(39,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16591);