Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,15)(10,19)(11,13)(12,26)(16,32)(17,27)(18,24)(20,35)(21,28)(22,37)(23,36)(25,29)(30,34)(33,38);(8,9)(10,20)(11,24)(12,27)(13,15)(14,18)(16,22)(17,29)(19,34)(21,33)(23,30)(25,31)(26,39)(28,35)(32,36)(37,38);(8,10)(9,16,18,20)(11,23)(12,28)(13,21)(14,22)(15,30,24,33)(17,35,27,32)(19,26)(25,37)(29,36)(31,34,39,38)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6392);