Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3486 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21)(22,26)(23,33)(24,36)(25,29)(27,35)(28,39)(30,47)(31,45)(32,42)(34,46)(37,41)(38,44)(40,49)(43,50)(48,51);(13,16)(17,19)(20,22,25,32)(21,26,29,42)(23,30,34,48)(24,37,39,31)(27,43,44,40)(28,45,36,41)(33,47,46,51)(35,50,38,49);(12,14,15,18)(13,17,16,19)(20,23)(21,27)(22,30)(24,38)(25,34)(26,40)(28,46)(29,44)(31,50)(32,48)(33,36)(35,39)(37,49)(41,51)(42,43)(45,47);(13,16)(17,19)(23,34)(27,44)(30,48)(33,46)(35,38)(40,43)(47,51)(49,50)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17011);