Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18994 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3153 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(20,21)(22,32)(23,36)(24,31)(25,30)(26,29)(27,34)(28,37)(33,41)(35,44)(38,45)(39,42)(40,43)(46,48)(47,50)(49,51);(14,18)(16,19)(20,22)(21,27)(23,33)(24,39)(25,34)(26,35)(28,41)(29,42)(30,44)(31,32)(36,50)(37,48)(38,49)(40,47)(43,51)(45,46);(12,13)(14,19)(15,17)(16,18)(20,23,26,38)(21,28,29,43)(22,33,35,49)(24,37,25,40)(27,41,42,51)(30,36,31,45)(32,46,44,50)(34,47,39,48);(21,29)(27,42)(28,43)(30,31)(32,44)(36,45)(41,51)(46,50)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11982);