Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3019 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1170 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)(14,18)(15,25)(16,29)(17,21)(19,28)(20,31)(22,37)(23,39)(24,34)(26,42)(27,36)(30,35)(32,38)(33,41)(40,43);(12,14,17,24)(13,18,21,34)(15,26)(16,23,31,41)(19,32)(20,33,29,39)(22,27)(25,37)(28,40)(30,38)(35,43)(36,42);(12,15)(13,19)(14,22)(16,30)(17,27)(18,32)(20,36)(21,35)(23,40)(24,26)(25,29)(28,31)(33,42)(34,43)(37,39)(38,41);(16,31)(20,29)(23,41)(25,36)(28,30)(33,39)(37,42)(38,40)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16988);