Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11126 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #390 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17)(18,28)(19,33,37,24)(20,27)(21,25)(22,26)(23,30)(29,44,46,41)(31,39)(32,40)(34,47,45,38)(35,42,36,43);(12,13,14,15)(16,18,20,30,22,32,21,31)(17,23,25,28,26,39,27,40)(19,34,35,29,37,45,36,46)(24,41,42,38,33,44,43,47);(16,19)(17,24)(18,29)(20,36)(21,35)(22,37)(23,38)(25,43)(26,33)(27,42)(28,41)(30,34)(31,45)(32,46)(39,47)(40,44)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4114);