Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19001 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
960 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)(11,17)(12,16)(13,15)(14,19)(20,23)(21,22)(24,25)(26,32)(27,35)(28,30)(29,33)(31,37)(34,39)(36,38);(8,10)(9,14)(11,21)(12,19)(13,20)(15,22)(16,23)(17,18)(24,26,28,34)(25,29,30,38)(27,36,37,33)(31,39,35,32);(8,10)(9,14)(11,19)(12,21)(13,20)(15,22)(16,18)(17,23)(27,37)(31,35)(32,39)(33,36);(9,15)(14,22)(16,17)(18,23)(25,30)(29,38)(31,35)(32,39)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11989);