Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10951 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #386 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1437 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
916 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18,23,33)(15,25)(16,28)(17,20)(19,27)(21,30)(22,36,38,39)(24,35,29,32)(26,40)(31,42,43,37)(34,41);(12,14)(13,18,20,33)(15,22)(16,29)(17,23)(19,31,34,43)(21,35,28,32)(24,30)(25,39,40,36)(26,38)(27,42)(37,41);(12,15,16,27,17,26,30,41)(13,19,21,25,20,34,28,40)(14,22,29,42,23,38,24,37)(18,31,35,39,33,43,32,36)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3939);