Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C2×C42 |
| direct product | C11×#7944 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#95 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C42×C11 ◁ G | |
604 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21)(15,19)(16,25)(17,20)(18,22)(23,26)(24,27)(28,29)(30,36,38,33)(31,34)(32,35)(37,42,39,41)(40,43);(12,14)(13,18,20,27)(15,24)(16,22)(17,23)(19,21,25,26)(28,30)(29,33)(31,39)(32,38)(34,42)(35,36)(37,40)(41,43);(12,15,17,16)(13,19,20,25)(14,22,23,24)(18,26,27,21)(28,31,32,40)(29,34,35,43)(30,37,38,39)(33,41,36,42)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 932);