Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18866 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3035 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
942 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,15)(18,19)(20,21)(22,30)(23,26)(24,28)(25,29)(27,31)(32,35)(33,34);(12,13,16,19)(14,17,15,18)(21,26)(23,24)(27,34)(28,29)(30,35)(31,32);(20,22)(21,27)(23,31)(24,32)(25,33)(26,34)(28,30)(29,35);(12,14,16,15)(13,18,19,17)(20,23,25,24)(21,26,29,28)(22,31,33,32)(27,34,35,30)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11872);