Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10061 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
534 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)(16,17,21,24)(18,25,27,30)(19,23,20,28)(22,29,31,26)(32,33,37,41)(34,42,45,46)(35,38,36,40)(39,43,47,44);(12,13)(14,15)(16,18,21,27)(17,22,24,31)(19,26,20,29)(23,30,28,25)(33,38)(35,36)(39,46)(40,41)(42,47)(43,44);(13,15)(16,19,21,20)(17,23,24,28)(18,26,27,29)(22,30,31,25)(32,34,37,45)(33,39,41,47)(35,44,36,43)(38,46,40,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3049);