Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24283 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24283 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1304 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)(16,17)(18,30)(19,34)(20,24)(21,28)(22,27)(23,29)(25,36)(26,33)(31,45)(32,40)(35,44)(37,43)(38,42)(39,46)(41,47);(12,13)(14,15)(16,18,21,20,23,33,22,32)(17,24,27,30,29,40,28,26)(19,31,36,35,37,46,38,47)(25,39,34,44,42,45,43,41);(13,15)(16,19)(17,25)(18,31)(20,35)(21,36)(22,38)(23,37)(24,39)(26,41)(27,34)(28,43)(29,42)(30,44)(32,47)(33,46)(40,45);(16,20,21,33,23,32,22,18)(17,26,27,24,29,30,28,40)(19,35,36,46,37,47,38,31)(25,41,34,39,42,44,43,45)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17271);