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×#19054 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3150 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
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)(22,32)(23,37)(24,29)(25,30)(26,31)(27,35)(28,39)(33,41)(34,42)(36,45)(38,43)(40,44)(46,48)(47,50)(49,51);(14,18)(16,19)(20,22)(21,27)(23,33)(24,34)(25,35)(26,36)(28,41)(29,32)(30,45)(31,42)(37,50)(38,47)(39,48)(40,49)(43,51)(44,46);(12,13)(14,19)(15,17)(16,18)(20,23,26,40)(21,28,31,43)(22,33,36,49)(24,39,25,38)(27,41,42,51)(29,44,30,37)(32,46,45,50)(34,48,35,47);(20,24,26,25)(21,29,31,30)(22,34,36,35)(23,38,40,39)(27,32,42,45)(28,37,43,44)(33,47,49,48)(41,50,51,46)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12042);