Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23414 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1980 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)(14,22)(15,19)(16,28)(17,21)(18,24)(20,30)(23,38)(25,36)(26,34)(27,42)(29,32)(31,43)(33,40)(35,41)(37,39);(12,14)(13,18)(15,23)(16,29)(17,25)(19,33)(20,36)(21,32)(22,28)(24,30)(26,39)(27,43)(31,34)(35,37)(38,42)(40,41);(12,15)(13,19)(14,23)(16,27)(17,26)(18,31)(20,35)(21,34)(22,37)(24,40)(25,39)(28,42)(29,43)(30,41)(32,33)(36,38);(15,26)(19,34)(23,39)(27,41)(31,33)(35,42)(37,38)(40,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16402);