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×#18883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3499 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
1096 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)(12,13,16,19)(14,18,15,17)(20,21,26,29)(22,30,27,35)(23,31,33,32)(24,28,25,34);(13,17)(14,15)(18,19)(20,22,26,27)(21,23,29,33)(24,32,25,31)(28,35,34,30);(20,23)(21,27)(22,29)(24,30)(25,35)(26,33)(28,32)(31,34);(12,14,16,15)(13,17,19,18)(20,24,26,25)(21,28,29,34)(22,31,27,32)(23,30,33,35)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11871);