Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19745 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19754 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3184 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
728 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)(8,9,12,14)(10,16,18,23)(11,20,17,15)(13,21,22,19)(24,25)(26,32)(27,29)(28,36)(30,34)(31,35)(33,38)(37,39);(8,10,17,21,12,18,11,19)(9,13,20,23,14,22,15,16)(25,29)(30,37)(31,36)(32,38);(9,14)(13,22)(15,20)(16,23)(24,26,28,34,27,33,35,39)(25,30,31,32,29,37,36,38);(10,18)(13,22)(16,23)(19,21)(26,33)(30,37)(32,38)(34,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12742);