Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33662 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C22×D8 |
| prime radical | C11×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
558 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)(22,26)(23,27)(24,37)(25,30)(28,34)(29,35)(31,38)(32,47)(33,41)(36,43)(39,44)(40,45)(42,48)(46,50)(49,51);(13,16)(17,19)(20,22,25,33)(21,26,30,41)(23,31,36,46)(24,32,35,45)(27,38,43,50)(28,39,42,49)(29,40,37,47)(34,44,48,51);(21,27)(23,34)(24,35)(26,38)(28,29)(30,43)(31,44)(32,45)(36,48)(37,42)(39,40)(41,50)(46,51)(47,49);(12,14,15,18)(13,17,16,19)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26650);