Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28×C4 |
| direct product | C11×#60649 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
3178 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)(13,15)(16,17)(18,26)(19,24)(20,32)(21,23)(22,28)(25,33)(27,39)(29,38)(30,36)(31,44)(34,42)(35,41)(37,43)(40,46)(45,47);(16,18,20,28,21,29,33,42)(17,22,25,26,23,34,32,38)(19,27,31,41,30,40,43,47)(24,35,37,39,36,45,44,46);(12,13,14,15)(17,23)(22,34)(24,36)(25,32)(26,38)(35,45)(37,44)(39,46);(16,19)(17,24)(18,27)(20,31)(21,30)(22,35)(23,36)(25,37)(26,39)(28,41)(29,40)(32,44)(33,43)(34,45)(38,46)(42,47);(19,30)(24,36)(27,40)(31,43)(35,45)(37,44)(39,46)(41,47)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53637);