Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#60161 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C4 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C23×D4 |
| prime radical | C2×C11×#575 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ G | |
2706 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,27)(19,24)(20,25)(21,34)(22,26)(23,29)(28,41)(30,37)(31,39)(32,40)(33,44)(35,38)(36,43)(42,47)(45,46);(16,18)(17,23)(19,28)(20,29)(21,35)(22,30)(24,36)(25,37)(26,38)(27,34)(31,42)(32,43)(33,45)(39,46)(40,47)(41,44);(12,14,15,13)(16,19)(17,24)(18,28)(20,32)(21,33)(22,31)(23,36)(25,40)(26,39)(27,41)(29,43)(30,42)(34,44)(35,45)(37,47)(38,46);(19,31)(24,39)(28,42)(32,33)(36,46)(40,44)(41,47)(43,45);(16,20,22,21)(17,25,26,34)(18,29,30,35)(19,32,31,33)(23,37,38,27)(24,40,39,44)(28,43,42,45)(36,47,46,41)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53149);