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×#24422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1300 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)(12,13,18,22,17,15,19,23)(14,20,27,35,26,29,28,24)(16,21,32,36,31,30,33,37)(25,34,40,38,39,42,41,43);(12,14,17,26)(13,20,15,29)(16,25,31,39)(18,28,19,27)(21,34,30,42)(22,24,23,35)(32,41,33,40)(36,43,37,38);(12,15)(13,17)(14,24)(16,30)(18,22)(19,23)(20,28)(21,31)(25,38)(26,35)(27,29)(32,36)(33,37)(34,40)(39,43)(41,42);(12,16)(13,21)(14,25)(15,30)(17,31)(18,33)(19,32)(20,34)(22,37)(23,36)(24,38)(26,39)(27,41)(28,40)(29,42)(35,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17410);