Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19802 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#1621 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ G | |
608 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,16)(14,21,23,27)(15,20,17,24)(19,26,25,22)(28,29,32,36)(30,33,38,42)(31,34,39,35)(37,40,43,41);(12,14,18,23)(13,19,16,25)(15,22,17,26)(20,27,24,21)(28,30,32,38)(29,33,36,42)(31,37,39,43)(34,40,35,41);(12,15,18,17)(13,20,16,24)(14,22,23,26)(19,27,25,21)(29,34)(31,39)(33,40)(35,36)(37,43)(41,42);(12,16,18,13)(14,21,23,27)(15,24,17,20)(19,26,25,22)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12790);