Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11365 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #121 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G | |
634 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,23)(19,21)(20,22)(24,25,28,33,29,31,27,32)(26,34,35,38,37,30,36,39);(12,13)(14,15)(16,18,20,19)(17,21,22,23)(24,26)(25,30)(27,35)(28,36)(29,37)(31,34)(32,39)(33,38);(13,15)(16,19,20,18)(17,21,22,23)(25,31)(26,35)(27,28)(30,38)(34,39)(36,37)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4353);