Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11709 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | C2×#102 |
| prime radical | C11×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18,19,16)(15,17)(20,21,23,28,26,31,25,30)(22,32,35,46,36,49,33,48)(24,38,37,29,41,45,40,47)(27,39,43,34,44,50,42,51);(12,14)(13,16)(15,19)(17,18)(20,22)(21,27)(23,33)(24,39)(25,35)(26,36)(28,42)(29,46)(30,43)(31,44)(32,45)(34,40)(37,51)(38,49)(41,50)(47,48);(20,23,26,25)(21,28,31,30)(22,33,36,35)(24,37,41,40)(27,42,44,43)(29,45,47,38)(32,48,49,46)(34,39,51,50)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4697);