Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
890 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)(13,15)(16,17)(18,23,29,38)(19,31)(20,27)(21,26)(22,25)(24,33)(28,42,44,45)(30,41,35,37)(32,39)(34,40)(36,46,47,43);(16,18,21,30,22,29,20,35)(17,23,27,37,25,38,26,41)(19,28,34,43,32,44,33,46)(24,36,39,42,40,47,31,45);(12,13,14,15)(16,19,20,33,22,32,21,34)(17,24,26,31,25,40,27,39)(18,28,35,46,29,44,30,43)(23,36,41,45,38,47,37,42)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3940);