Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#20829 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C22×C4⋊C4 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ G | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,25,29,26,30,24,40)(22,27,34,43,32,42,33,49)(23,35,38,45,39,51,37,28)(31,46,48,44,36,50,47,41);(13,16)(17,19)(20,22)(21,27)(23,36)(24,33)(25,34)(26,32)(28,44)(29,43)(30,42)(31,39)(35,50)(37,48)(38,47)(40,49)(41,45)(46,51);(20,23,24,37,26,39,25,38)(21,28,29,35,30,45,40,51)(22,31,33,47,32,36,34,48)(27,41,43,46,42,44,49,50);(12,14,15,18)(13,17,16,19)(22,32)(27,42)(31,36)(33,34)(41,44)(43,49)(46,50)(47,48)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13817);