Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32878 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#32961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
1320 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)(16,17,19,21)(18,22,23,20)(24,25,28,30)(26,33,35,39)(27,32,29,36)(31,37,38,34);(16,18,19,23)(17,20,21,22)(25,30)(31,38)(32,36)(33,39);(24,26)(25,31)(27,34)(28,35)(29,37)(30,38)(32,39)(33,36);(13,15)(24,27,28,29)(25,32,30,36)(26,34,35,37)(31,39,38,33)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25949);