Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10279 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,22,19)(18,26,30,27)(20,25,21,24)(23,29,31,28)(32,33,36,39)(34,40,42,47)(35,43,45,38)(37,44,46,41);(13,15)(16,18,22,30)(17,23,19,31)(20,29,21,28)(24,27,25,26);(16,19,22,17)(18,27,30,26)(20,24,21,25)(23,28,31,29)(32,34,36,42)(33,37,39,46)(35,44,45,41)(38,47,43,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3267);