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×#61088 |
| 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 | |
2714 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)(16,17,22,27)(18,28,32,45)(19,24,35,43)(20,26,21,25)(23,37,40,31)(29,39,33,47)(30,38,46,41)(34,44,36,42);(16,18)(17,23)(19,33)(20,31)(21,37)(22,32)(24,41)(25,28)(26,45)(27,40)(29,35)(30,34)(36,46)(38,43)(39,42)(44,47);(13,15)(16,19)(17,24)(18,29)(20,36)(21,34)(22,35)(23,38)(25,44)(26,42)(27,43)(28,39)(30,31)(32,33)(37,46)(40,41)(45,47);(16,19)(17,24)(18,30)(20,34)(21,36)(22,35)(23,39)(25,42)(26,44)(27,43)(28,38)(29,31)(32,46)(33,37)(40,47)(41,45);(16,20,22,21)(17,25,27,26)(18,31,32,37)(19,34,35,36)(23,28,40,45)(24,42,43,44)(29,46,33,30)(38,47,41,39)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54076);