Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24421 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1310 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)(12,13,18,32,17,19,16,22)(14,23,31,20,26,34,24,33)(15,27,29,36,30,21,28,37)(25,38,39,42,40,43,41,35);(13,19)(14,24)(16,18)(20,34)(21,27)(23,33)(25,39)(26,31)(28,29)(35,43)(38,42)(40,41);(12,14)(13,20)(15,25)(16,31)(17,26)(18,24)(19,33)(21,35)(22,34)(23,32)(27,42)(28,39)(29,41)(30,40)(36,38)(37,43);(12,15)(13,21)(14,25)(16,29)(17,30)(18,28)(19,27)(20,35)(22,37)(23,38)(24,39)(26,40)(31,41)(32,36)(33,42)(34,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17409);