Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23903 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C11×#3485 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1744 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)(16,17,21,25)(18,22,28,35)(19,23,30,37)(20,31,32,24)(26,38,40,33)(27,41,42,34)(29,36,43,44)(39,46,47,45);(12,13)(14,15)(16,18,21,28)(17,22,25,35)(19,26,30,40)(20,27,32,42)(23,33,37,38)(24,34,31,41)(29,39,43,47)(36,45,44,46);(13,15)(16,19)(17,23)(18,26)(20,29)(21,30)(22,33)(24,36)(25,37)(27,39)(28,40)(31,44)(32,43)(34,45)(35,38)(41,46)(42,47);(16,20)(17,24)(18,27)(19,29)(21,32)(22,34)(23,36)(25,31)(26,39)(28,42)(30,43)(33,45)(35,41)(37,44)(38,46)(40,47)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16893);