Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61350 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3035 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#533 ◁ G | |
1746 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)(17,18)(20,21,25,30)(22,32,34,27)(23,36,38,45)(24,31,26,29)(28,40,43,37)(33,47,48,51)(35,42,39,44)(41,50,46,49);(12,13,15,16)(14,18,19,17)(20,22,25,34)(21,27,30,32)(23,33,38,48)(24,39,26,35)(28,41,43,46)(29,44,31,42)(36,51,45,47)(37,50,40,49);(20,23)(21,28)(22,33)(24,37)(25,38)(26,40)(27,41)(29,36)(30,43)(31,45)(32,46)(34,48)(35,49)(39,50)(42,47)(44,51);(12,14,15,19)(13,17,16,18)(22,34)(27,32)(33,48)(35,39)(41,46)(42,44)(47,51)(49,50);(20,24,25,26)(21,29,30,31)(22,35,34,39)(23,37,38,40)(27,42,32,44)(28,36,43,45)(33,49,48,50)(41,47,46,51)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54338);