Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1942 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)(14,15)(16,17)(18,27)(19,24)(20,25)(21,34)(22,26)(23,29)(28,43)(30,37)(31,40)(32,42)(33,41)(35,38)(36,46)(39,44)(45,47);(16,18)(17,23)(19,28)(20,29)(21,35)(22,30)(24,39)(25,37)(26,38)(27,34)(31,44)(32,46)(33,45)(36,41)(40,47)(42,43);(13,15)(16,19,22,33)(17,24,26,41)(18,28,30,45)(20,32,21,31)(23,36,38,39)(25,42,34,40)(27,43,37,47)(29,46,35,44);(16,20,22,21)(17,25,26,34)(18,29,30,35)(19,31,33,32)(23,37,38,27)(24,40,41,42)(28,44,45,46)(36,43,39,47)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16391);