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×#24001 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3020 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1122 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)(14,19)(15,26)(16,21)(17,32)(18,23)(20,30)(22,35)(24,40)(25,31)(27,43)(28,42)(29,39)(33,37)(34,38)(36,41);(12,14,18,21)(13,19,23,16)(15,27)(17,25,35,38)(20,36)(22,34,32,31)(24,29)(26,40)(28,37)(30,42)(33,41)(39,43);(12,15)(13,20)(14,24)(16,28)(17,33)(18,29)(19,36)(21,27)(22,39)(23,37)(25,42)(26,32)(30,35)(31,40)(34,43)(38,41);(12,16,18,19)(13,21,23,14)(15,28,29,36)(17,34,35,31)(20,27,37,24)(22,25,32,38)(26,41,39,42)(30,40,33,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16989);