Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#8980 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #120 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C2×C11×#459 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
692 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,21,22,20,18,19,23)(25,28,29,31);(12,13,14,15)(16,18,20,17)(19,23,21,22)(26,30)(28,31);(16,19,20,21)(17,22,18,23)(24,25,27,29)(26,31,30,28)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1968);