Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18287 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C25×C11 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1064 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21)(14,22,25,35)(15,26,29,20)(17,19,30,34)(18,27,32,23)(24,36,38,43)(28,39,41,33)(31,40,42,37);(12,14,16,25)(13,18,21,32)(15,27,29,23)(17,24,30,38)(19,31,34,42)(20,35,26,22)(28,40,41,37)(33,43,39,36);(15,28)(20,33)(22,36)(23,37)(26,39)(27,40)(29,41)(35,43);(13,19)(18,31)(20,33)(21,34)(22,36)(26,39)(32,42)(35,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11275);