Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
552 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)(10,13)(11,14)(12,15)(16,19)(17,20)(18,22)(21,23)(24,25,29,33)(26,34,37,38)(27,30,28,32)(31,35,39,36);(8,10,12,17)(9,13,15,20)(11,16,18,23)(14,21,22,19)(25,30)(27,28)(31,38)(32,33)(34,39)(35,36);(8,11)(9,14)(10,16)(12,18)(13,19)(15,22)(17,23)(20,21)(24,26,29,37)(25,31,33,39)(27,36,28,35)(30,38,32,34)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2949);