Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#8486 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #379 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#3559 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(9,13,15,18)(14,22,23,21)(24,25,28,32,29,33,27,37)(26,34,35,30,36,31,38,39);(8,9)(10,14)(11,18)(12,15)(13,20)(16,21)(17,23)(19,22)(24,26)(25,30)(27,38)(28,35)(29,36)(31,32)(33,39)(34,37);(8,10,12,17)(9,14,15,23)(11,19,20,16)(13,21,18,22)(24,26)(25,31)(27,35)(28,38)(29,36)(30,32)(33,34)(37,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1474);