Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61052 |
| 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 ◁ C11×#525 ◁ G | |
2722 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)(14,15)(16,17)(18,26)(19,23)(20,33)(21,24)(22,29)(25,34)(27,40)(28,37)(30,36)(31,44)(32,38)(35,42)(39,45)(41,47)(43,46);(16,18,21,30)(17,22,24,37)(19,27,32,43)(20,28,34,29)(23,35,38,47)(25,36,33,26)(31,41,45,42)(39,46,44,40);(13,15)(16,19,21,32)(17,23,24,38)(18,27,30,43)(20,31,34,45)(22,35,37,47)(25,39,33,44)(26,40,36,46)(28,41,29,42);(18,28)(20,34)(22,36)(25,33)(26,37)(27,41)(29,30)(31,45)(35,46)(39,44)(40,47)(42,43);(17,24)(22,37)(23,38)(25,33)(26,36)(35,47)(39,44)(40,46)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54040);