Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33552 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C11 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G | |
1156 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)(23,35)(24,36)(26,32)(27,33)(28,41)(29,34)(30,38)(31,39)(37,43)(40,42);(12,14)(13,18)(15,23)(16,25)(17,24)(19,30)(20,22)(21,31)(26,38)(27,37)(28,40)(29,39)(32,35)(33,42)(34,36)(41,43);(12,15,17,27)(13,19,21,33)(14,23,24,37)(16,28,29,26)(18,30,31,42)(20,32,34,41)(22,35,36,43)(25,40,39,38);(14,24)(18,31)(22,36)(23,37)(25,39)(30,42)(35,43)(38,40)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26540);