Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22455 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#22455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#576 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1378 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)(15,27,29,19)(16,30)(17,21)(18,25)(20,31)(23,37,40,36)(24,34)(26,33)(28,35,43,42)(32,39,41,38);(12,14)(13,18)(15,23)(16,24)(17,26)(19,32)(20,33)(21,34)(22,30)(25,31)(27,41)(28,38)(29,40)(35,37)(36,42)(39,43);(12,15)(13,19)(14,23)(16,28)(17,29)(18,32)(20,35)(21,27)(22,36)(24,38)(25,39)(26,40)(30,42)(31,43)(33,37)(34,41);(14,24)(16,31)(18,33)(20,30)(22,34)(23,38)(25,26)(28,43)(32,37)(35,42)(36,41)(39,40)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15443);