Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9380 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
424 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)(14,22,15,18)(16,21)(17,20)(19,24,26,23)(25,27)(28,29,32,36,33,37,31,35)(30,38,40,34,41,42,39,43);(12,14,16,15)(13,18)(17,24,25,23)(19,20)(21,22)(26,27)(28,30)(29,34)(31,40)(32,39)(33,41)(35,42)(36,38)(37,43);(12,15,16,14)(13,19,21,26)(17,23,25,24)(18,20,22,27)(28,30)(29,34)(31,39)(32,40)(33,41)(35,38)(36,42)(37,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2368);