Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18250 |
| 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 | |
932 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)(15,26)(19,30)(20,29)(21,27)(24,34)(28,36)(31,37)(32,40)(33,41)(38,39)(42,43);(12,13,16,21)(14,19,22,31)(15,27,26,18)(17,20,23,32)(24,37,34,30)(25,33,35,43)(28,40,36,29)(38,41,39,42);(14,22)(15,28)(18,29)(19,31)(24,38)(25,35)(26,36)(27,40)(30,42)(33,43)(34,39)(37,41);(12,14,23,35)(13,19,32,43)(15,24,36,38)(16,22,17,25)(18,30,40,42)(20,33,21,31)(26,34,28,39)(27,37,29,41)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11238);