Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#34526 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C25 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
1800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,24)(19,21)(20,27)(22,25)(23,28)(26,29)(30,31)(32,33,36,39)(34,40,42,37)(35,38,43,45)(41,46,47,44);(17,19)(18,25)(23,27)(26,31)(32,33,36,39)(34,37,42,40)(35,38,43,45)(41,44,47,46);(12,13,15,14)(16,18)(17,22)(19,24)(20,26)(21,25)(23,29)(27,30)(28,31)(32,33)(34,37)(35,38)(36,39)(40,42)(41,44)(43,45)(46,47);(16,19,21,17)(18,24,25,22)(20,27,28,23)(26,30,31,29)(32,34)(33,37)(35,41)(36,42)(38,44)(39,40)(43,47)(45,46);(12,14,15,13)(16,20)(17,23)(18,26)(19,27)(21,28)(22,29)(24,30)(25,31)(32,35,36,43)(33,38,39,45)(34,41,42,47)(37,44,40,46)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 27514);