Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,15,19)(16,25,26,20)(18,24,27,23)(28,29)(30,33)(31,34)(32,36)(35,40)(37,41)(38,43)(39,42);(12,14,17,15)(13,18,21,27)(16,24,26,23)(19,25,22,20)(28,30,32,38)(29,33,36,43)(31,39,40,37)(34,42,35,41);(12,15,17,14)(13,19,21,22)(16,23,26,24)(18,20,27,25)(29,34)(31,40)(33,41)(35,36)(37,39)(42,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3284);