Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61096 |
| 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×#532 ◁ G | |
2686 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)(16,17,21,25)(18,23,28,40)(19,24,32,42)(20,33,36,26)(22,34,38,29)(27,39,45,41)(30,47,46,37)(31,44,35,43);(16,18)(17,22)(19,30)(20,34)(21,28)(23,33)(24,41)(25,38)(26,40)(27,31)(29,36)(32,46)(35,45)(37,43)(39,42)(44,47);(13,15)(16,18)(17,23)(19,27)(20,29)(21,28)(22,33)(24,39)(25,40)(26,38)(30,31)(32,45)(34,36)(35,46)(37,43)(41,42)(44,47);(16,19,21,32)(17,24,25,42)(18,27,28,45)(20,35,36,31)(22,37,38,47)(23,39,40,41)(26,44,33,43)(29,46,34,30);(17,25)(18,28)(24,42)(26,33)(27,45)(29,34)(30,46)(43,44)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54084);