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×#26372 |
| 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 | |
864 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)(16,17,20,22)(18,21,19,23)(24,25)(26,33)(27,30)(28,32)(29,34)(31,37)(35,39)(36,38);(12,13)(14,15)(16,18,20,19)(17,21,22,23)(24,26,28,35)(25,29,32,38)(27,36,37,34)(30,33,31,39);(13,15)(16,19,20,18)(17,21,22,23);(25,30)(27,37)(29,33)(31,32)(34,36)(38,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 19360);