Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#18255 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1260 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)(16,19)(20,21,25,30)(22,27,32,35)(23,29,24,28)(26,33,34,31);(12,13)(14,16)(15,17)(18,19)(20,22)(21,26)(23,31)(24,33)(25,32)(27,28)(29,35)(30,34);(12,14)(13,16)(15,18)(17,19)(20,22)(21,27)(23,33)(24,31)(25,32)(26,28)(29,34)(30,35);(20,23,25,24)(21,28,30,29)(22,31,32,33)(26,27,34,35)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11243);