Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24181 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3036 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
1050 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)(14,18)(15,16)(17,19)(20,21)(22,30)(23,29)(24,28)(25,27)(26,32)(31,35)(33,34);(13,16)(17,18)(20,22,24,32)(21,26,28,30)(23,31,25,33)(27,35,29,34);(21,27)(23,25)(26,34)(28,29)(30,35)(31,33);(12,14,15,19)(13,17,16,18)(20,23,24,25)(21,27,28,29)(22,31,32,33)(26,35,30,34)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17169);