Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33747 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
512 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)(20,21,25,29)(22,30,32,44)(23,35,37,50)(24,38,36,28)(26,39,40,33)(27,42,43,31)(34,49,48,46)(41,47,45,51);(13,16)(17,19);(20,22,31,47,24,34,37,39,25,32,42,51,36,48,23,33)(21,26,35,46,28,41,43,44,29,40,50,49,38,45,27,30);(12,14,15,18)(13,17,16,19)(22,32)(26,40)(30,44)(33,39)(34,48)(41,45)(46,49)(47,51)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26735);