Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60666 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C2×C11×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
1762 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17)(14,18,19,16)(20,21,24,26)(22,30,32,43)(23,28,34,39)(25,37,36,29)(27,40,38,33)(31,44,45,51)(35,48,47,42)(41,50,49,46);(12,14,15,19)(13,16,17,18)(21,26)(27,38)(28,39)(29,37)(30,43)(41,49)(42,48)(44,51);(20,22,25,33,24,32,36,40)(21,27,29,30,26,38,37,43)(23,31,35,46,34,45,47,50)(28,41,42,44,39,49,48,51);(20,23)(21,28)(22,31)(24,34)(25,35)(26,39)(27,41)(29,42)(30,44)(32,45)(33,46)(36,47)(37,48)(38,49)(40,50)(43,51);(23,34)(28,39)(31,45)(35,47)(41,49)(42,48)(44,51)(46,50)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53654);