Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10356 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,11,13)(10,14,15,12)(16,17)(18,20)(19,22)(21,23)(24,25,27,30)(26,34,36,39)(28,33,29,32)(31,35,38,37);(8,10,11,15)(9,12,13,14)(25,30)(26,35)(28,29)(31,34)(36,37)(38,39);(17,20)(18,23)(21,22)(24,26,27,36)(25,31,30,38)(28,35,29,37)(32,39,33,34)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3344);