Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18377 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3490 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1082 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)(12,13,16,21)(14,23,24,36)(15,27,30,20)(17,22,31,19)(18,28,33,25)(26,38,39,43)(29,35,42,37)(32,41,34,40);(12,14)(13,18)(15,28)(16,24)(17,26)(19,34)(20,36)(21,33)(22,32)(23,27)(25,30)(29,41)(31,39)(35,38)(37,43)(40,42);(15,29)(20,37)(23,38)(25,40)(27,35)(28,41)(30,42)(36,43);(13,19)(14,24)(18,32)(20,35)(21,22)(23,38)(25,28)(26,39)(27,37)(33,34)(36,43)(40,41)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11365);