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×#13336 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
586 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)(16,17)(18,29)(19,23)(20,36)(21,39)(22,28)(24,31)(25,33)(26,37)(27,35)(30,42)(32,41)(34,43)(38,46)(40,45)(44,47);(12,13)(14,15)(17,23)(18,30)(19,33)(20,37)(21,35)(24,42)(25,27)(26,39)(28,36)(29,46)(31,47)(32,40)(41,43)(44,45);(13,15)(16,18)(17,24)(19,34)(20,38)(21,40)(22,32)(23,41)(25,42)(26,45)(27,46)(28,44)(29,36)(30,35)(31,37)(33,47)(39,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6324);