Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61477 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#529 ◁ G | |
1772 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)(13,16)(17,19)(20,21,26,30)(22,27,33,42)(23,35,37,43)(24,29,25,38)(28,39,44,36)(31,45,47,50)(32,41,34,48)(40,49,51,46);(12,13)(14,17)(15,16)(18,19)(20,22,26,33)(21,27,30,42)(23,31,37,47)(24,32,25,34)(28,40,44,51)(29,41,38,48)(35,45,43,50)(36,46,39,49);(20,23)(21,28)(22,31)(24,36)(25,39)(26,37)(27,40)(29,43)(30,44)(32,46)(33,47)(34,49)(35,38)(41,50)(42,51)(45,48);(13,16)(17,19)(20,24,26,25)(21,29,30,38)(22,32,33,34)(23,36,37,39)(27,41,42,48)(28,43,44,35)(31,46,47,49)(40,50,51,45);(12,14,15,18)(13,17,16,19)(22,33)(27,42)(31,47)(32,34)(40,51)(41,48)(45,50)(46,49)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54465);