Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×C11×#327 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C22⋊C4 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C23×C11 | C2×C22⋊C4 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C22×C42×C11 ◁ G | |
816 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31);(6,10,11,18)(7,14)(12,19,13,15)(16,20);(5,6)(7,15)(8,12)(9,13)(10,16)(11,17)(14,18)(19,20)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1202);