Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20954 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,21,27,22,25,20,26)(18,28,32,23,31,39,30,38)(19,33,35,40,36,24,34,41)(29,42,45,46,44,47,43,37);(12,13,14,15)(16,18)(17,23)(19,29)(20,32)(21,30)(22,31)(24,37)(25,38)(26,39)(27,28)(33,46)(34,45)(35,43)(36,44)(40,42)(41,47);(16,19,22,36)(17,24,25,33)(18,29,31,44)(20,35,21,34)(23,37,38,46)(26,41,27,40)(28,42,39,47)(30,45,32,43);(17,25)(23,38)(24,33)(26,27)(28,39)(37,46)(40,41)(42,47)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13942);