Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23918 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24010 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C25×C11 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G | |
1428 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 704 |
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)(19,20)(22,23)(24,25,29,32)(26,30,28,36)(27,34,35,38)(31,37,39,33);(12,13)(14,15)(17,20)(21,23)(24,26,29,28)(25,30,32,36)(27,33,35,37)(31,38,39,34);(13,15)(16,18,19,22)(17,21,20,23)(24,27)(25,31)(26,33)(28,37)(29,35)(30,38)(32,39)(34,36);(17,20)(21,23)(24,26,29,28)(25,30,32,36)(27,33,35,37)(31,38,39,34)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16998);