Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33541 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
1104 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)(13,19)(14,24)(15,17)(16,27)(20,35)(21,28)(22,33)(23,34)(25,40)(26,31)(29,30)(32,36)(37,43)(38,41);(12,13)(14,20)(15,21)(16,28)(17,22)(18,23)(19,27)(24,36)(25,41)(26,38)(29,34)(30,33)(31,37)(32,39)(35,40)(42,43);(12,14)(13,20)(15,24)(16,25)(17,31)(18,26)(19,32)(21,36)(22,37)(23,38)(27,39)(28,41)(29,42)(30,40)(33,35)(34,43);(12,15,18,17)(13,21,23,22)(14,24,26,31)(16,27,30,29)(19,33,34,28)(20,36,38,37)(25,39,40,42)(32,35,43,41)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26529);