Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
418 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,16,13,17,11,15)(10,18,20,14,21,22,19,23)(24,25,29,31,28,27,33,36)(26,32,34,39,35,30,37,38);(8,10)(9,14)(11,20)(12,19)(13,21)(15,22)(16,18)(17,23)(24,26,33,34,28,35,29,37)(25,30,31,39,27,32,36,38);(8,10)(9,14)(11,19)(12,20)(13,21)(15,18)(16,22)(17,23)(24,27)(25,28)(26,32)(29,31)(30,35)(33,36)(34,38)(37,39)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2363);