Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19050 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19051 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3545 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(20,21,26,31)(22,32,35,44)(23,36,37,45)(24,30,25,29)(27,39,42,34)(28,40,43,38)(33,41,47,51)(46,48,50,49);(14,18)(16,19)(20,22)(21,27)(23,33)(24,39)(25,34)(26,35)(28,41)(29,44)(30,32)(31,42)(36,50)(37,47)(38,49)(40,48)(43,51)(45,46);(12,13)(14,19)(15,17)(16,18)(20,23)(21,28)(22,33)(24,38)(25,40)(26,37)(27,41)(29,36)(30,45)(31,43)(32,46)(34,48)(35,47)(39,49)(42,51)(44,50);(23,37)(28,43)(33,47)(36,45)(38,40)(41,51)(46,50)(48,49)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12039);