Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#22035 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C23×C4 |
| prime radical | C11×#2388 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,22)(19,21)(20,23)(24,25,29,26,28,31,36,33)(27,30,35,32,34,37,39,38);(16,18)(17,20)(19,23)(21,22)(24,26,29,31,28,33,36,25)(27,32,35,37,34,38,39,30);(13,15)(18,23)(20,22)(24,27)(25,30)(26,32)(28,34)(29,35)(31,37)(33,38)(36,39);(17,21)(20,22)(27,34)(30,37)(32,38)(35,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15023);