Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23917 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1682 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,23)(19,31)(20,25)(21,36)(22,27)(24,34)(26,29)(28,41)(30,40)(32,47)(33,43)(35,39)(37,42)(38,45)(44,46);(12,13)(14,15)(16,18,22,30)(17,23,27,40)(19,28,33,44)(20,21,35,29)(24,38,42,47)(25,36,39,26)(31,46,43,41)(32,37,45,34);(13,15)(16,19)(17,24)(18,28)(20,32)(21,37)(22,33)(23,38)(25,41)(26,43)(27,42)(29,34)(30,44)(31,36)(35,45)(39,46)(40,47);(16,20,22,35)(17,25,27,39)(18,29,30,21)(19,32,33,45)(23,26,40,36)(24,41,42,46)(28,34,44,37)(31,38,43,47)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16905);