Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C2×D4 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C23×C11 | C4×D4 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ C23×C8×C11 ◁ G | |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,23)(19,21)(20,22)(25,29,31,35)(26,32,34,36);(13,15)(16,18,20,19)(17,21,22,23)(24,25,28,31)(26,33,34,38)(27,35,37,29)(30,36,39,32);(13,15)(16,19,20,18)(17,21,22,23)(24,26,28,34)(25,30,31,39)(27,36,37,32)(29,38,35,33)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4364);