Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18425 |
| 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 | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,18,15)(14,24,28,38)(16,22,17,30)(19,23,35,31)(20,33,25,26)(21,34,29,32)(27,40,42,36)(37,43,41,39);(12,14,18,28)(13,20,15,25)(16,26,17,33)(19,27,35,42)(21,36,29,40)(22,38,30,24)(23,37,31,41)(32,39,34,43);(12,15,18,13)(14,25,28,20)(16,21,17,29)(19,31,35,23)(22,34,30,32)(24,39,38,43)(26,36,33,40)(27,41,42,37);(12,16,18,17)(13,21,15,29)(14,26,28,33)(19,32,35,34)(20,36,25,40)(22,31,30,23)(24,37,38,41)(27,39,42,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11413);