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×#61500 |
| 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 | |
1794 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)(13,16)(17,19)(20,21)(22,31)(23,35)(24,29)(25,30)(26,40)(27,34)(28,37)(32,48)(33,44)(36,51)(38,46)(39,43)(41,47)(42,49)(45,50);(12,13)(14,17)(15,16)(18,19)(20,22)(21,27)(23,36)(24,39)(25,34)(26,33)(28,45)(29,44)(30,31)(32,38)(35,48)(37,49)(40,43)(41,50)(42,47)(46,51);(20,23)(21,28)(22,32)(24,37)(25,38)(26,41)(27,42)(29,46)(30,47)(31,45)(33,49)(34,36)(35,40)(39,50)(43,51)(44,48);(13,16)(17,19)(20,24,25,26)(21,29,30,40)(22,33,34,39)(23,37,38,41)(27,43,31,44)(28,46,47,35)(32,49,36,50)(42,51,45,48);(12,14,15,18)(13,17,16,19)(22,34)(27,31)(32,36)(33,39)(42,45)(43,44)(48,51)(49,50)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54488);