Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9213 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #386 |
| prime radical | C11×#3106 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19,17,20,15,25)(14,21,24,26,22,27,23,18)(29,33,35,38)(30,36,37,39);(12,14)(13,18,20,26)(15,23)(16,24)(17,22)(19,21,25,27)(28,29,31,38,32,35,40,33)(30,34,39,42,37,43,36,41);(14,22)(18,26)(21,27)(23,24)(28,30)(29,34)(31,39)(32,37)(33,41)(35,43)(36,40)(38,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2201);