Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C22×C11×#501 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C11 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ C22×C42×C11 ◁ G | |
2142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6,8,10)(7,11,12,9)(14,17)(15,19)(18,20);(5,7,8,12)(6,9,10,11)(14,18)(17,20);(13,14,15,17,16,18,19,20)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53644);