Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24769 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
946 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)(13,14)(20,21,26,34,25,30,24,29)(22,27,31,35,23,33,32,28);(12,13,15,14)(16,17)(18,19)(20,22)(21,27)(23,25)(24,32)(26,31)(28,29)(30,33)(34,35);(17,19)(20,23,25,22)(21,28,30,35)(24,32,26,31)(27,34,33,29);(12,14,15,13)(20,24,25,26)(21,29,30,34)(22,31,23,32)(27,35,33,28)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17757);