Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18987 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| socle | C22×C7 | C2×#120 |
| prime radical | C7×#3529 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C42×C7 ◁ G | |
904 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18)(11,20)(12,15)(13,16)(14,17)(19,22)(21,23)(24,25,29,32)(26,33,35,38)(27,31,28,36)(30,37,39,34);(8,10)(9,11)(12,19)(13,20)(14,21)(15,18)(16,23)(17,22)(24,26)(25,30)(27,34)(28,37)(29,35)(31,38)(32,39)(33,36);(8,11)(9,10)(12,18)(13,23)(14,22)(15,19)(16,20)(17,21)(24,25)(26,30)(27,31)(28,36)(29,32)(33,37)(34,38)(35,39);(8,12,14,13)(9,15,17,16)(10,19,21,20)(11,18,22,23)(24,27,29,28)(25,31,32,36)(26,34,35,37)(30,38,39,33)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11975);