Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1146 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)(22,27)(23,34)(24,29)(25,38)(26,30)(28,36)(31,47)(32,41)(33,43)(35,45)(37,46)(39,42)(40,48)(44,50)(49,51);(12,14,15,19)(13,16,17,18)(20,22)(21,27)(23,31)(24,32)(25,39)(26,33)(28,44)(29,41)(30,43)(34,47)(35,48)(36,50)(37,49)(38,42)(40,45)(46,51);(20,23,26,37)(21,28,30,45)(22,31,33,49)(24,36,25,35)(27,40,43,44)(29,46,38,34)(32,50,39,48)(41,47,42,51);(20,24,26,25)(21,29,30,38)(22,32,33,39)(23,35,37,36)(27,41,43,42)(28,34,45,46)(31,48,49,50)(40,51,44,47)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16452);