Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18372 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3493 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
904 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)(12,13,16,19)(14,20,21,27)(15,23,25,18)(17,24,26,22)(29,34)(31,32)(35,42)(36,37)(38,40)(41,43);(12,14)(13,17)(15,24)(16,21)(18,27)(19,26)(20,23)(22,25)(28,29)(30,35)(31,34)(32,36)(33,37)(38,41)(39,43)(40,42);(28,30,33,39)(29,35,37,43)(31,38,32,40)(34,41,36,42);(14,21)(17,26)(20,27)(22,24)(28,31,33,32)(29,36,37,34)(30,38,39,40)(35,42,43,41)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11360);