Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33735 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C22×D8 |
| prime radical | C11×#2215 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
526 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
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)(22,27)(23,33)(24,38)(25,40)(26,30)(28,35)(29,34)(31,44)(32,43)(36,50)(37,47)(39,51)(41,45)(42,49)(46,48);(13,16)(17,19)(20,22,26,25)(21,27,30,40)(23,31,37,36)(24,32,39,34)(28,41,42,46)(29,38,43,51)(33,44,47,50)(35,45,49,48);(20,23,34,48,25,36,39,49,26,37,32,45,22,31,24,35)(21,28,38,44,27,41,43,47,30,42,51,50,40,46,29,33);(12,14,15,18)(13,17,16,19)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26723);