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) = C24×C4 |
| direct product | C11×#22265 |
| 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×#2397 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
962 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)(13,15)(16,17)(18,21)(19,22)(20,23)(24,25,29,33,28,32,27,31)(26,30,34,37,35,38,36,39);(16,18,21,17)(19,22,20,23)(24,25,27,31,28,32,29,33)(26,30,36,39,35,38,34,37);(12,13,14,15)(16,19,21,20)(17,22,18,23)(24,26,28,35)(25,30,32,38)(27,36,29,34)(31,39,33,37);(16,20,21,19)(17,22,18,23)(24,27,28,29)(25,31,32,33)(26,34,35,36)(30,37,38,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15253);