Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10944 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #390 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,27)(19,32)(20,36)(21,25)(22,26)(23,29)(24,33)(28,37)(30,39)(31,38)(34,40)(35,46)(41,43)(42,45)(44,47);(16,18,21,29,22,31,20,30)(17,23,25,38,26,39,36,27)(19,28,34,42,35,44,33,43)(24,37,32,45,40,47,46,41);(13,15)(16,19,20,33,22,35,21,34)(17,24,25,32,26,40,36,46)(18,28,30,43,31,44,29,42)(23,37,38,45,39,47,27,41)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3932);