Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#19213 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C23×C7 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,16)(10,17,15,12)(11,14,19,21)(18,23,22,20)(24,25)(26,32)(27,29)(28,36)(30,34)(31,35)(33,39)(37,38);(8,10,12,9,13,15,17,16)(11,18,20,14,19,22,23,21)(25,29)(30,38)(31,36)(32,39);(8,11)(9,14)(10,18)(12,20)(13,19)(15,22)(16,21)(17,23)(24,26,27,33)(25,30,29,38)(28,37,35,34)(31,39,36,32);(11,19)(14,21)(18,22)(20,23)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12201);