Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19215 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
582 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,17)(16,24)(18,22)(19,23)(21,27)(25,26)(28,29,33,36)(30,37,35,32)(31,38,39,43)(34,40,42,41);(13,17)(18,26)(19,24)(20,27)(28,30,32,29,33,35,37,36)(31,38,40,34,39,43,41,42);(12,14,15,21)(13,18,17,26)(16,25,23,22)(19,27,24,20)(28,31,33,39)(29,34,36,42)(30,38,35,43)(32,40,37,41);(31,39)(34,42)(38,43)(40,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12203);