Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18208 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#1595 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
994 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)(19,32)(20,30)(21,27)(23,31)(25,36)(28,39)(33,42)(34,40)(37,41);(12,13)(14,23)(15,27)(16,21)(17,20)(18,26)(19,22)(24,31)(25,37)(28,40)(29,34)(30,39)(32,35)(33,36)(38,41)(42,43);(15,28)(18,30)(24,38)(26,39)(27,40)(31,41)(32,42)(35,43);(12,14,17,25)(13,19,20,33)(15,24,28,38)(16,22,29,36)(18,31,30,41)(21,23,34,37)(26,35,39,43)(27,32,40,42)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11196);