Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23814 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C11×#376 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,19,20)(18,21,22,23)(24,25,28,32,29,33,43,49)(26,34,37,45,36,47,41,30)(27,38,39,46,40,48,42,31)(35,44,52,55,51,54,53,50);(12,13)(14,15)(17,20)(21,23)(24,26,29,36)(25,30,33,45)(27,35,40,51)(28,41,43,37)(31,44,46,54)(32,47,49,34)(38,50,48,55)(39,53,42,52);(13,15)(24,27,29,40)(25,31,33,46)(26,35,36,51)(28,42,43,39)(30,44,45,54)(32,48,49,38)(34,50,47,55)(37,53,41,52);(16,18,19,22)(17,21,20,23)(26,36)(30,45)(34,47)(35,51)(37,41)(44,54)(50,55)(52,53)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16802);