Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60761 |
| 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 ◁ C22×C11×#41 ◁ G | |
2140 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)(20,21,26,30)(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);(12,14)(13,16)(15,19)(17,18)(20,22)(21,27)(23,31)(24,32)(25,34)(26,33)(28,40)(29,41)(30,42)(35,45)(36,46)(37,47)(38,48)(39,49)(43,50)(44,51);(14,19)(16,18)(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);(13,17)(16,18)(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);(22,33)(27,42)(31,47)(32,34)(40,51)(41,48)(45,50)(46,49)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53749);