Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2199 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33550 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C11 |
| socle | C2×C11 | C2×B(4,𝔽2) |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G | |
1144 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)(14,22)(15,19)(16,20)(17,21)(18,25)(23,34)(24,35)(26,31)(27,32)(28,33)(29,37)(30,38)(36,42)(39,41)(40,43);(12,14)(13,18)(15,24)(16,25)(17,23)(19,30)(20,22)(21,29)(26,38)(27,36)(28,37)(31,35)(32,40)(33,34)(39,43)(41,42);(14,23)(16,28)(18,29)(22,34)(24,36)(26,39)(30,40)(35,42);(12,15,17,27)(13,19,21,32)(14,24,23,36)(16,26,28,39)(18,30,29,40)(20,31,33,41)(22,35,34,42)(25,38,37,43)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26538);