Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60454 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60620 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
2014 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)(20,21,26,31)(22,32,34,43)(23,37,38,45)(24,30,25,29)(27,36,42,35)(28,39,44,40)(33,41,47,51)(46,48,50,49);(13,16)(17,19)(20,22,25,36,26,34,24,35)(21,27,30,43,31,42,29,32)(23,33,40,49,38,47,39,48)(28,41,37,50,44,51,45,46);(12,14,15,18)(13,17,16,19)(20,23,24,39,26,38,25,40)(21,28,29,45,31,44,30,37)(22,33,35,48,34,47,36,49)(27,41,32,46,42,51,43,50);(23,38)(28,44)(33,47)(37,45)(39,40)(41,51)(46,50)(48,49);(22,34)(27,42)(32,43)(33,47)(35,36)(41,51)(46,50)(48,49)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53608);