Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13414 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,22,27)(18,28,31,46)(19,23,21,25)(20,33,36,43)(24,39,42,29)(26,32,44,34)(30,40,37,45)(35,41,47,38);(17,23)(18,29)(19,21)(20,34)(24,40)(25,27)(26,44)(28,38)(30,35)(31,39)(32,36)(37,47)(41,46)(42,45);(13,15)(16,18,19,30,22,31,21,37)(17,24,25,41,27,42,23,38)(20,35,32,29,36,47,34,39)(26,40,43,28,44,45,33,46)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6402);