Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#20776 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#117 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#383 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C7×M16 ◁ G | |
684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,19)(11,23,25,30)(12,17)(13,18)(14,22)(15,24,31,37)(16,26)(20,27,33,38)(21,29)(28,35)(32,34,36,39);(8,10,13,21)(9,14)(11,20,25,33)(12,22,26,35)(15,27)(16,19)(17,29)(18,28)(23,36)(24,34,37,39)(30,32)(31,38);(8,11,12,24,13,25,26,37)(9,15,16,30,18,31,17,23)(10,20,22,34,21,33,35,39)(14,27,19,32,28,38,29,36);(10,21)(14,28)(19,29)(20,33)(22,35)(27,38)(32,36)(34,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13764);