Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33745 |
| 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 ◁ C11×#117 ◁ C11×#405 ◁ G | |
496 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)(20,21,24,29)(22,31,35,46)(23,28,26,38)(25,41,40,48)(27,42,32,36)(30,39,44,33)(34,45,37,51)(43,49,47,50);(13,16)(17,19)(20,21)(22,32)(23,38)(24,29)(25,30)(26,28)(27,35)(31,42)(33,41)(34,43)(36,46)(37,47)(39,48)(40,44)(45,50)(49,51);(20,22,33,49,26,37,40,42,24,35,39,50,23,34,25,36)(21,27,41,45,28,43,44,46,29,32,48,51,38,47,30,31);(12,14,15,18)(13,17,16,19)(20,23,24,26)(21,28,29,38)(22,34,35,37)(25,39,40,33)(27,43,32,47)(30,41,44,48)(31,45,46,51)(36,50,42,49)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26733);