Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33729 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C23×C11 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17)(14,18,19,16)(22,30)(23,31)(24,34)(26,36)(28,37)(29,41)(32,46)(33,44)(35,45)(38,47)(39,51)(40,50)(42,43)(48,49);(12,14,15,19)(13,16,17,18)(20,21)(22,26)(23,28)(24,29)(25,27)(30,36)(31,37)(32,39)(33,38)(34,41)(35,40)(42,48)(43,49)(44,47)(45,50)(46,51);(20,22,31,43,24,32,35,44,25,33,45,46,34,42,23,30)(21,26,37,49,29,39,40,47,27,38,50,51,41,48,28,36);(21,27)(26,38)(28,40)(29,41)(36,47)(37,50)(39,48)(49,51)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26717);