Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#60108 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C4 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C23×D4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C22×C11×#41 ◁ G | |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,27)(19,24)(20,25)(21,35)(22,26)(23,30)(28,40)(29,37)(31,41)(32,38)(33,39)(34,45)(36,44)(42,47)(43,46);(16,18,21,30,22,31,20,29)(17,23,25,27,26,37,35,41)(19,28,34,44,32,42,33,43)(24,36,39,40,38,46,45,47);(16,19)(17,24)(18,28)(20,33)(21,34)(22,32)(23,36)(25,39)(26,38)(27,40)(29,43)(30,44)(31,42)(35,45)(37,46)(41,47);(19,32)(24,38)(28,42)(33,34)(36,46)(39,45)(40,47)(43,44);(16,20,22,21)(17,25,26,35)(18,29,31,30)(19,33,32,34)(23,27,37,41)(24,39,38,45)(28,43,42,44)(36,40,46,47)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53096);