Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18453 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,18)(16,19)(20,26)(21,24)(22,25)(23,27)(28,29,33,36)(30,37,39,42)(31,35,32,40)(34,41,43,38);(12,14)(13,17)(15,20)(16,21)(18,23)(19,24)(22,27)(25,26)(28,30,33,39)(29,34,36,43)(31,38,32,41)(35,42,40,37);(12,15)(13,18)(14,20)(16,22)(17,23)(19,25)(21,27)(24,26)(31,32)(35,40)(37,42)(38,41);(13,19)(17,24)(18,25)(23,26)(28,31,33,32)(29,35,36,40)(30,38,39,41)(34,42,43,37)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11441);