Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#32699 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2749 |
| 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 | |
538 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)(12,13,18,23,17,22,30,38)(14,15,20,27,25,19,31,34)(16,21,29,37,28,36,32,39)(24,33,40,43,41,26,35,42);(12,14)(13,19)(15,22)(16,24)(17,25)(18,31)(20,30)(21,26)(23,27)(28,41)(29,35)(32,40)(33,36)(34,38)(37,43)(39,42);(12,15)(13,20,22,31)(14,23,25,38)(16,26)(17,19)(18,27)(21,35,36,40)(24,39,41,37)(28,33)(29,42)(30,34)(32,43);(12,16,17,28)(13,21,22,36)(14,24,25,41)(15,26,19,33)(18,32,30,29)(20,35,31,40)(23,39,38,37)(27,43,34,42)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25687);