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×#18415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3534 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
992 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)(12,13,16,20)(14,18,21,25)(15,17,23,19)(22,24,27,26)(28,29)(30,33)(31,34)(32,35)(36,42)(37,40)(38,41)(39,43);(13,17)(15,23)(18,24)(19,20)(22,27)(25,26)(28,30)(29,33)(31,36)(32,37)(34,39)(35,40)(38,43)(41,42);(12,14)(13,18)(15,22)(16,21)(17,24)(19,26)(20,25)(23,27)(28,31)(29,34)(30,36)(32,38)(33,39)(35,41)(37,43)(40,42);(14,21)(18,25)(22,27)(24,26)(29,35)(33,40)(34,41)(39,42)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11403);