Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#25032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#466 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G | |
906 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)(16,17)(18,20)(19,21)(22,23)(24,25)(26,31)(27,36)(28,38)(29,33)(30,34)(32,37)(35,39);(12,13)(14,15)(16,18,19,22)(17,20,21,23)(24,26,28,34,29,35,37,27)(25,30,32,31,33,36,38,39);(13,15)(17,21)(20,23);(24,27,37,35,29,34,28,26)(25,31,38,30,33,39,32,36)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 18020);