Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33684 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
546 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)(14,17)(15,16)(18,19)(20,21)(22,31)(23,28)(24,27)(25,38)(26,32)(29,37)(30,36)(33,44)(34,41)(35,42)(39,47)(40,51)(43,50)(45,49)(46,48);(13,16)(17,19)(20,22,23,32)(21,26,28,31)(24,33,35,47)(25,34,36,48)(27,39,42,44)(29,40,43,45)(30,41,38,46)(37,49,50,51);(21,27)(24,37)(25,36)(26,39)(28,42)(29,30)(31,44)(33,49)(34,48)(35,50)(38,43)(40,41)(45,46)(47,51);(12,14,15,18)(13,17,16,19)(22,32)(26,31)(33,47)(34,48)(39,44)(40,45)(41,46)(49,51)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26672);