Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23535 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#394 |
| prime radical | C2×C11×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1352 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)(14,23)(15,28)(16,33)(17,21)(18,22)(19,25)(20,31)(24,34)(26,36)(27,35)(29,37)(30,41)(32,38)(39,42)(40,43);(12,14)(13,19)(15,29)(16,26)(17,25)(18,27)(20,37)(21,35)(22,36)(23,33)(24,32)(28,34)(30,40)(31,39)(38,43)(41,42);(12,15,16,31,18,30,17,32)(13,20,21,28,22,38,33,41)(14,24,25,40,27,39,26,29)(19,34,23,37,36,42,35,43);(15,30)(20,38)(24,39)(28,41)(29,40)(31,32)(34,42)(37,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16523);