Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18283 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(17,23)(24,27)(28,29,32,34)(30,36,38,43)(31,39,41,35)(33,40,42,37);(12,13)(14,17)(15,18)(16,19)(20,24)(21,23)(22,25)(26,27)(28,30,32,38)(29,33,34,42)(31,40,41,37)(35,43,39,36);(12,14)(13,17)(15,20)(16,21)(18,24)(19,23)(22,26)(25,27)(28,29)(30,33)(31,39)(32,34)(35,41)(36,40)(37,43)(38,42);(12,15,16,22)(13,18,19,25)(14,20,21,26)(17,24,23,27)(29,34)(33,42)(35,39)(36,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11271);