Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23474 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #393 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| socle | C2×C11 | C2×#393 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,25,28,19)(16,20)(17,21)(22,35,26,30)(23,31)(24,32)(27,38,40,33)(29,34)(36,43,39,41)(37,42);(12,14)(13,18)(15,26,28,22)(16,23)(17,24)(19,30,25,35)(20,31)(21,32)(27,39,40,36)(29,37)(33,41,38,43)(34,42);(12,15)(13,19)(14,22)(16,27)(17,28)(18,30)(20,33)(21,25)(23,36)(24,26)(29,40)(31,41)(32,35)(34,38)(37,39)(42,43);(12,16,17,29)(13,20,21,34)(14,23,24,37)(15,27,28,40)(18,31,32,42)(19,33,25,38)(22,36,26,39)(30,41,35,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16462);