Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18385 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3505 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1012 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)(12,13,18,15)(14,24,29,39)(16,22,17,31)(19,23,35,32)(20,26,25,27)(21,33,30,34)(28,38,43,36)(37,42,41,40);(12,14)(13,20)(15,25)(16,27)(17,26)(18,29)(19,28)(21,38)(22,39)(23,37)(24,31)(30,36)(32,41)(33,40)(34,42)(35,43);(12,15,18,13)(14,25,29,20)(16,30,17,21)(19,32,35,23)(22,34,31,33)(24,40,39,42)(26,38,27,36)(28,41,43,37);(12,16,18,17)(13,21,15,30)(14,26,29,27)(19,33,35,34)(20,36,25,38)(22,23,31,32)(24,37,39,41)(28,42,43,40)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11373);