Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#21939 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C25×C11 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G | |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 704 |
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)(26,30)(27,34)(28,37)(29,32)(31,35)(33,38)(36,39);(16,18)(17,20)(19,23)(21,22)(24,26,29,28)(25,30,32,37)(27,33,36,35)(31,34,38,39);(18,23)(20,22)(24,27,28,35,29,36,26,33)(25,31,30,34,32,38,37,39);(17,21)(20,22)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14927);