Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#21478 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#120 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C4×#120 |
| prime radical | C11×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C8×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)(12,13,18,23,19,24,17,30)(14,25,28,20,29,39,34,38)(15,21,31,16,22,32,35,33)(26,27,41,43,37,40,42,36);(12,14)(13,20)(15,26)(16,27)(17,34)(18,28)(19,29)(21,36)(22,37)(23,39)(24,38)(25,30)(31,41)(32,43)(33,40)(35,42);(12,15)(13,21)(14,26)(16,23)(17,35)(18,31)(19,22)(20,36)(24,32)(25,40)(27,39)(28,41)(29,37)(30,33)(34,42)(38,43);(12,16,18,32,19,33,17,21)(13,22,23,35,24,15,30,31)(14,27,28,43,29,40,34,36)(20,37,39,42,38,26,25,41)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14466);