Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23646 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×#121 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
906 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)(20,21,24,29,26,31,25,30)(22,27,33,42,34,43,40,47)(23,35,38,46,39,45,37,28)(32,44,36,50,49,51,48,41);(13,16)(17,19)(20,22)(21,27)(23,36)(24,33)(25,40)(26,34)(28,44)(29,42)(30,47)(31,43)(32,37)(35,50)(38,49)(39,48)(41,45)(46,51);(12,14,15,18)(13,17,16,19)(20,23)(21,28)(22,32)(24,37)(25,38)(26,39)(27,41)(29,45)(30,35)(31,46)(33,48)(34,49)(36,40)(42,51)(43,50)(44,47);(20,24,26,25)(21,29,31,30)(22,33,34,40)(23,37,39,38)(27,42,43,47)(28,45,46,35)(32,48,49,36)(41,51,50,44)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16634);