Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(17,24)(18,30)(19,35)(20,38)(21,22)(25,42)(26,29)(27,36)(28,39)(32,40)(33,37)(34,46)(41,43)(45,47);(12,13)(14,15)(16,17,23,29)(18,31,34,44)(19,36,20,39)(21,28,22,27)(24,38,26,35)(25,33,42,32)(30,43,46,47)(37,45,40,41);(13,15)(16,18)(17,25)(19,37)(20,40)(21,33)(22,32)(23,34)(24,41)(26,45)(27,44)(28,31)(29,42)(30,38)(35,46)(36,47)(39,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6325);