Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11130 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
862 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)(12,13,14,15)(16,17)(18,27)(19,24)(20,36)(21,25)(22,26)(23,29)(28,39)(30,44)(31,38)(32,47)(33,42)(34,40)(35,41)(37,45)(43,46);(16,18,20,29,22,30,21,31)(17,23,25,27,26,38,36,44)(19,32,33,28,35,45,34,46)(24,39,40,47,41,43,42,37);(16,19,22,35)(17,24,26,41)(18,28,30,46)(20,34,21,33)(23,37,38,47)(25,42,36,40)(27,43,44,39)(29,32,31,45)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4118);