Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#32950 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1282 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)(16,29)(20,31)(21,32)(23,39)(24,25)(26,27)(30,34)(33,42)(36,37)(38,40);(12,13,16,18,17,21,29,32)(14,19,24,30,25,35,22,34)(15,20,26,31,28,37,27,36)(23,33,39,41,40,42,38,43);(12,14)(13,19)(15,23)(16,24)(17,25)(18,30)(20,33)(21,35)(22,29)(26,39)(27,38)(28,40)(31,41)(32,34)(36,43)(37,42);(12,15)(13,20)(14,23)(16,26)(17,28)(18,31)(19,33)(21,37)(22,38)(24,39)(25,40)(27,29)(30,41)(32,36)(34,43)(35,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25938);