Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12741 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#12741 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1786 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,23,25,19)(15,18)(16,30)(17,21)(20,27)(22,28)(24,36,41,31)(26,35,40,38)(29,32)(33,42)(34,39,37,43);(13,18)(15,27)(16,28)(19,31)(20,22)(21,32)(23,36)(24,39)(26,40)(29,42)(30,33)(34,35)(37,38)(41,43);(12,14)(13,19)(15,24)(16,26)(17,25)(18,31)(20,34)(21,23)(22,35)(27,39)(28,40)(29,41)(30,38)(32,36)(33,37)(42,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5729);