Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
568 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)(20,21,26,31)(22,27,34,45)(23,29,25,41)(24,37,40,51)(28,46,48,33)(30,36,49,39)(32,42,35,44)(38,43,50,47);(13,16)(17,19)(20,22)(21,27)(23,35)(24,33)(25,32)(26,34)(28,37)(29,44)(30,43)(31,45)(36,50)(38,39)(40,46)(41,42)(47,49)(48,51);(12,14,15,18)(13,17,16,19)(20,22)(21,28)(23,32)(24,38)(25,35)(26,34)(27,37)(29,43)(30,44)(31,48)(33,39)(36,46)(40,50)(41,47)(42,49)(45,51);(20,23,26,25)(21,29,31,41)(22,32,34,35)(24,36,40,39)(27,42,45,44)(28,43,48,47)(30,37,49,51)(33,38,46,50)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26641);