Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#25985 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
842 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)(12,13,15,17)(14,18,19,16)(20,21)(22,32)(23,27)(24,30)(25,31)(26,35)(28,37)(29,41)(33,46)(34,43)(36,44)(38,47)(39,48)(40,45)(42,49)(50,51);(20,22,25,36)(21,26,31,45)(23,34,39,49)(24,40,41,35)(27,46,48,51)(28,43,47,42)(29,44,30,32)(33,37,50,38);(12,14,15,19)(13,16,17,18)(20,23)(21,27)(22,33)(24,37)(25,39)(26,42)(28,30)(29,47)(31,48)(32,46)(34,40)(35,49)(36,50)(38,41)(43,45)(44,51);(20,23)(21,28)(22,34)(24,38)(25,39)(26,43)(27,30)(29,48)(31,47)(32,46)(33,40)(35,50)(36,49)(37,41)(42,45)(44,51)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 18973);