Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
2026 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)(14,18)(15,17)(16,19)(20,21,25,30)(22,26,31,39)(23,28,34,42)(24,27,36,29)(32,38,44,49)(33,40,45,37)(35,41,47,43)(46,50,51,48);(12,14,15,19)(13,16,17,18)(20,22)(21,26)(23,32)(24,33)(25,31)(27,40)(28,38)(29,37)(30,39)(34,44)(35,46)(36,45)(41,50)(42,49)(43,48)(47,51);(14,19)(16,18)(21,27)(22,31)(24,36)(26,37)(28,41)(29,30)(32,44)(35,47)(38,48)(39,40)(42,43)(49,50);(13,17)(16,18)(20,23)(21,28)(22,32)(24,35)(25,34)(26,38)(27,41)(29,43)(30,42)(31,44)(33,46)(36,47)(37,48)(39,49)(40,50)(45,51);(23,34)(28,42)(32,44)(35,47)(38,49)(41,43)(46,51)(48,50)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53814);