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×#24868 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#2407 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G | |
1018 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)(16,17)(18,20)(19,21)(22,23)(26,33)(30,38)(34,39)(35,37);(13,15)(16,18,19,22)(17,20,21,23)(24,25)(26,34)(27,31)(28,32)(29,36)(30,35)(33,39)(37,38);(17,21)(20,23)(24,26,28,33)(25,30,32,38)(27,35,29,37)(31,39,36,34);(13,15)(24,27,28,29)(25,31,32,36)(26,35,33,37)(30,39,38,34)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17856);