Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C25×C4 |
| direct product | C11×#10716 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C42 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | C2×#95 |
| prime radical | C25×C11 | D4 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ G | |
1414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,24,26,30)(19,22)(20,23)(21,25,28,31)(27,29);(16,18)(17,21,23,28)(19,25)(20,26)(22,24,29,30)(27,31);(13,15)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3704);