Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9307 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9313 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C42 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#3115 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
428 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)(8,9,12,15,13,16,11,21)(10,17,20,22,18,23,19,14)(24,25,29,33,30,32,28,26)(27,34,36,31,37,35,38,39);(8,10)(9,14,16,22)(11,19)(12,20)(13,18)(15,17,21,23)(24,26,29,32,30,33,28,25)(27,35,36,31,37,34,38,39);(10,18)(14,22)(17,23)(19,20)(24,27)(25,31)(26,34)(28,38)(29,36)(30,37)(32,39)(33,35)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2301);