Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19142 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×#121 |
| prime radical | C11×#3100 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,17)(18,19)(20,21)(22,29)(23,27)(24,33)(25,28)(26,32)(30,35)(31,34);(13,16)(17,18)(20,22,24,32,25,30,23,31)(21,26,27,29,28,34,33,35);(13,17)(15,19)(16,18)(22,30)(26,34)(29,35)(31,32);(20,23,25,24)(21,27,28,33)(22,31,30,32)(26,29,34,35)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12130);