Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#27040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C4×C7×C22⋊C4 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,15)(12,13)(16,17)(18,22)(19,20)(21,23)(24,25,27,30)(26,32,34,29)(28,31,36,38)(33,37,35,39);(9,13)(14,15)(17,20)(21,22)(24,26)(25,29)(27,34)(28,33)(30,32)(31,39)(35,36)(37,38);(8,10,12,11)(9,14,13,15)(16,18,19,23)(17,21,20,22)(25,30)(26,33)(28,36)(29,37)(32,39)(34,35);(8,11,12,10)(9,14,13,15)(17,20)(21,22)(25,30)(29,32)(31,38)(37,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 20028);