Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#24988 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#472 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
656 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)(15,27)(16,28)(20,35)(21,32)(25,26)(29,40)(30,34)(33,41)(36,38)(37,43);(12,13,16,18,17,21,28,32)(14,23,22,30,26,19,25,34)(15,20,27,31,29,35,40,42)(24,37,36,41,39,33,38,43);(12,14)(13,19)(15,24)(16,25)(17,26)(18,30)(20,33)(21,23)(22,28)(27,38)(29,39)(31,41)(32,34)(35,37)(36,40)(42,43);(12,15,28,40,17,29,16,27)(13,20,32,42,21,35,18,31)(14,24,22,36,26,39,25,38)(19,33,34,43,23,37,30,41)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17976);