Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#24525 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
858 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)(14,18)(15,17)(16,19)(20,21,24,29,26,31,25,30)(22,27,33,42,35,44,34,43)(23,36,40,28,39,47,38,46)(32,48,37,41,50,45,49,51);(12,14,15,19)(13,16,17,18)(20,22)(21,27)(23,37)(24,33)(25,34)(26,35)(28,45)(29,42)(30,43)(31,44)(32,38)(36,41)(39,49)(40,50)(46,48)(47,51);(20,23)(21,28)(22,32)(24,38)(25,40)(26,39)(27,41)(29,36)(30,47)(31,46)(33,49)(34,37)(35,50)(42,48)(43,45)(44,51);(13,17)(16,18)(20,24,26,25)(21,29,31,30)(22,33,35,34)(23,38,39,40)(27,42,44,43)(28,36,46,47)(32,49,50,37)(41,48,51,45)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17513);