Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#17387 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#121 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C4×D4×C11 ◁ G | |
984 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20,22,17)(15,18)(16,19)(21,26,27,24)(23,25)(28,29,31,34,32,35,38,41)(30,33,37,40,36,39,42,43);(12,14,16,22)(13,17,19,20)(15,21,23,27)(18,24,25,26)(28,30)(29,33)(31,37)(32,36)(34,40)(35,39)(38,42)(41,43);(12,15)(13,18)(14,21)(16,23)(17,24)(19,25)(20,26)(22,27)(30,36)(33,39)(37,42)(40,43);(15,23)(18,25)(21,27)(24,26)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10375);