Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C11 · Schur multiplier (H2) = C24×C42 |
| direct product | C11×#13779 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C11 | C24 |
| commutator | C22 | C22×C42×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1582 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(20,21,23,22)(24,25)(26,28)(27,30)(29,31);(16,17,18,19)(20,22,23,21)(25,26)(29,30);(12,13,14,15)(24,26,28,25)(27,30,31,29);(24,27,28,31)(25,29,26,30)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6767);