Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1946 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)(16,17,22,27)(18,28,30,40)(19,32,34,41)(20,26,21,25)(23,35,38,31)(24,36,39,33)(29,37,43,47)(42,44,46,45);(12,13)(14,15)(16,18)(17,23)(19,29)(20,35)(21,31)(22,30)(24,37)(25,40)(26,28)(27,38)(32,46)(33,45)(34,43)(36,44)(39,47)(41,42);(13,15)(16,19)(17,24)(18,29)(20,33)(21,36)(22,34)(23,37)(25,32)(26,41)(27,39)(28,42)(30,43)(31,44)(35,45)(38,47)(40,46);(18,30)(23,38)(28,40)(29,43)(31,35)(37,47)(42,46)(44,45)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16396);