Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9216 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #121 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2816 |
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)(17,20)(18,22)(21,23)(24,25,28,30,29,33,27,32)(26,34,36,31,37,38,35,39);(16,17,18,20,19,21,22,23)(25,30)(27,28)(31,34)(32,33)(35,36)(38,39);(13,15)(24,26,29,37)(25,31,33,39)(27,36,28,35)(30,34,32,38)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2204);