Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13396 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
422 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)(10,19)(11,24)(12,13)(15,29)(16,31)(17,28)(20,32)(21,36)(22,37)(23,25)(26,27)(30,39)(33,38)(34,35);(8,9)(10,20)(11,16)(12,28)(13,17)(14,18)(15,22)(19,35)(21,34)(23,30)(24,31)(25,29)(26,38)(27,33)(32,36)(37,39);(8,10,13,22,14,21,12,23)(9,15,17,34,18,30,28,20)(11,25,24,36,27,37,26,19)(16,32,31,39,33,35,38,29)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6384);