Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#22887 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C11×#3002 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×C22⋊C8 ◁ G | |
1020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,21,25,22,26,20,34)(18,27,29,23,30,38,35,39)(19,24,33,43,32,41,36,42)(28,44,46,37,45,40,31,47);(16,18,21,29,22,30,20,35)(17,23,25,38,26,39,34,27)(19,31,33,28,32,46,36,45)(24,40,43,47,41,44,42,37);(13,15)(19,32)(24,41)(28,45)(31,46)(33,36)(37,47)(40,44)(42,43);(16,19)(17,24)(18,28)(20,36)(21,33)(22,32)(23,37)(25,43)(26,41)(27,44)(29,46)(30,45)(31,35)(34,42)(38,40)(39,47)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15875);