Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#26161 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×D4×C11 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G | |
840 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)(18,21)(19,23)(20,22)(24,25)(26,31)(27,35)(28,30)(29,33)(32,34)(36,38)(37,39);(12,13)(14,15)(16,18,20,19)(17,21,22,23)(25,30)(26,28)(31,33)(32,35)(34,37)(38,39);(13,15)(16,19,20,18)(17,21,22,23)(24,26,29,28)(25,31,33,30)(27,34,36,37)(32,38,39,35);(24,27,29,36)(25,32,33,39)(26,34,28,37)(30,35,31,38)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 19149);