Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#24987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18)(14,22)(15,26)(16,28)(20,35)(21,31)(24,25)(27,39)(29,33)(32,40)(36,37)(42,43);(12,13,16,18,17,21,28,31)(14,19,22,33,25,34,24,29)(15,20,26,30,27,35,39,41)(23,32,36,42,38,43,37,40);(12,14)(13,19)(15,23)(16,24)(17,25)(18,29)(20,32)(21,34)(22,28)(26,37)(27,38)(30,40)(31,33)(35,43)(36,39)(41,42);(12,15,16,26,17,27,28,39)(13,20,18,30,21,35,31,41)(14,23,24,37,25,38,22,36)(19,32,29,40,34,43,33,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17975);