Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60454 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60705 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3455 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
1846 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 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)(22,26,31,39)(23,33,34,48)(24,36,37,28)(27,41,42,35)(30,43,44,51)(32,47,46,40)(38,49,50,45);(13,16)(17,19)(20,22,25,31)(21,26,29,39)(23,30,34,44)(24,32,37,46)(27,38,42,50)(28,40,36,47)(33,43,48,51)(35,45,41,49);(20,23,24,35,25,34,37,41)(21,27,28,33,29,42,36,48)(22,30,32,45,31,44,46,49)(26,38,40,43,39,50,47,51);(12,14,15,18)(13,17,16,19)(22,31)(26,39)(30,44)(32,46)(38,50)(40,47)(43,51)(45,49);(23,34)(27,42)(30,44)(33,48)(35,41)(38,50)(43,51)(45,49)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53693);