Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33767 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
564 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)(14,18)(15,17)(16,19)(22,30)(23,33)(24,35)(26,38)(28,43)(29,42)(31,48)(32,47)(34,37)(36,46)(39,50)(40,51)(41,49)(44,45);(12,14)(13,16)(15,19)(17,18)(20,21)(22,26)(23,28)(24,29)(25,27)(30,38)(31,40)(32,39)(33,43)(34,44)(35,42)(36,41)(37,45)(46,49)(47,50)(48,51);(14,19)(16,18)(20,22,25,32)(21,26,27,39)(23,34,36,48)(24,37,35,31)(28,44,41,51)(29,45,42,40)(30,46,47,33)(38,49,50,43);(13,17)(16,18)(21,27)(26,39)(28,41)(29,42)(38,50)(40,45)(43,49)(44,51)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26755);