Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18746 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18797 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3106 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
924 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)(10,17)(11,15)(12,20)(13,16)(14,18)(19,22)(21,23)(24,25)(26,35)(27,38)(28,34)(29,33)(30,32)(31,36)(37,39);(8,10,13,19)(9,14,16,23)(11,18,12,21)(15,22,20,17)(24,26,30,27)(25,31,32,39)(28,37,29,36)(33,38,34,35);(8,11,13,12)(9,15,16,20)(10,18,19,21)(14,22,23,17)(24,27,30,26)(25,31,32,39)(28,36,29,37)(33,38,34,35);(8,11,13,12)(9,15,16,20)(10,18,19,21)(14,22,23,17)(25,32)(31,39)(33,34)(35,38)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11785);