Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#22892 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×2−1+4 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17,23,29)(18,30,19,33)(20,26,38,44)(21,28,22,27)(24,35,25,32)(31,46,34,42)(36,41,47,40)(37,45,39,43);(12,14,15,13)(16,18,23,19)(17,24,29,25)(20,36,38,47)(21,35,22,32)(26,42,44,46)(27,33,28,30)(31,39,34,37)(40,45,41,43);(16,19,23,18)(17,25,29,24)(20,34,38,31)(21,35,22,32)(26,41,44,40)(27,33,28,30)(36,37,47,39)(42,43,46,45);(16,20)(17,26)(18,31)(19,34)(21,39)(22,37)(23,38)(24,40)(25,41)(27,45)(28,43)(29,44)(30,46)(32,47)(33,42)(35,36)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15880);