Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23847 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #401 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| socle | C2×C11 | C2×#401 |
| prime radical | C24×C11 | C24 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
604 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)(14,22,25,18)(15,19,28,34)(16,20)(17,21)(23,32)(24,36,38,31)(26,30)(27,33,40,43)(29,35)(37,42)(39,41);(12,14)(13,18)(15,26,28,23)(16,24)(17,25)(19,32,34,30)(20,31)(21,22)(27,39,40,37)(29,38)(33,42,43,41)(35,36);(12,15)(13,19,21,34)(14,23)(16,27)(17,28)(18,30,22,32)(20,33,35,43)(24,37)(25,26)(29,40)(31,41,36,42)(38,39);(12,16,17,29)(13,20,21,35)(14,24,25,38)(15,27,28,40)(18,31,22,36)(19,33,34,43)(23,37,26,39)(30,41,32,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16835);