Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23362 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2380 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3153 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
706 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)(14,18,24,34)(15,26,29,36)(16,22)(17,21)(19,30,37,39)(20,28)(23,35)(25,33,31,38)(27,32)(40,43)(41,42);(12,14)(13,18)(15,27)(16,24)(17,31)(19,35)(20,33)(21,38)(22,34)(23,39)(25,28)(26,32)(29,41)(30,40)(36,42)(37,43);(12,15,28,39,16,29,17,30)(13,19,21,26,22,37,20,36)(14,23,31,27,24,40,25,41)(18,32,33,35,34,42,38,43);(13,20,22,21)(14,24)(18,33,34,38)(19,36,37,26)(23,40)(25,31)(27,41)(32,35,42,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16350);