Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18282 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#1600 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
942 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)(19,31)(20,29)(21,27)(25,36)(28,37)(30,32)(33,40)(34,42)(41,43);(12,13,16,21)(14,19,22,32)(15,27,26,18)(17,20,23,33)(24,31,35,30)(25,34,36,43)(28,40,37,29)(38,41,39,42);(14,22)(15,28)(18,29)(19,32)(24,38)(25,36)(26,37)(27,40)(30,42)(31,41)(34,43)(35,39);(12,14,23,36)(13,19,33,43)(15,24,37,38)(16,22,17,25)(18,30,40,42)(20,34,21,32)(26,35,28,39)(27,31,29,41)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11270);