Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#33853 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×D4 ◁ C7×C8×D4 ◁ G | |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(13,18)(14,23)(15,24)(16,25)(19,30)(20,26)(21,36)(22,34)(28,29)(31,41)(32,33)(35,40)(37,43)(39,42);(12,13,17,21)(14,19,23,22)(15,26,28,42)(16,30,32,34)(18,33,36,25)(20,38,39,27)(24,35,29,43)(31,40,41,37);(9,11)(12,14,17,23)(13,19,21,22)(15,24,28,29)(16,25,32,33)(18,34,36,30)(20,37,39,40)(26,35,42,43)(27,41,38,31);(12,15,17,28)(13,20,21,39)(14,24,23,29)(16,31,32,41)(18,35,36,43)(19,37,22,40)(25,27,33,38)(26,34,42,30)385 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26841);