Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13332 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
566 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)(18,28)(19,24)(20,26)(21,37)(22,27)(23,30)(25,34)(29,38)(31,43)(32,45)(33,44)(35,41)(36,42)(39,47)(40,46);(13,15)(16,18,22,32)(17,23,27,40)(19,33,36,47)(20,29,21,31)(24,28,42,45)(25,43,41,38)(26,44,37,39)(30,35,46,34);(17,24)(18,29)(19,34)(20,21)(23,38)(25,26)(27,42)(28,44)(30,46)(31,32)(35,36)(37,41)(39,45)(40,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6320);