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) = C2×C43 |
| direct product | C11×#14641 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C24 | C24×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
1486 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)(25,28)(29,31)(32,33,35,36)(34,37,39,38);(17,20)(21,23)(25,28)(26,30)(33,36)(37,38);(16,17)(18,21)(19,20)(22,23)(24,25)(26,29)(27,28)(30,31)(32,33)(34,38)(35,36)(37,39);(16,18,19,22)(17,21,20,23)(24,26,27,30)(25,29,28,31)(32,34,35,39)(33,37,36,38)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 7629);