Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#7154 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | D8 |
| commutator | C8 | C4×C8×C11 |
| Frattini, cosocle | C2×C4×C8 | C22×C11 |
| socle, prime radical | C23×C11 | #107 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,18,20,19,21,22,23)(25,30)(26,34)(27,36)(28,35)(31,32)(33,39)(37,38);(13,15)(24,25,27,31,28,32,26,30,29,33,34,38,35,37,36,39)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 142);