Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33691 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#33692 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C7×#405 ◁ G | |
536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(10,18)(11,22)(12,26)(14,27)(16,31)(17,30)(19,24)(20,35)(21,36)(23,37)(25,38)(28,39)(29,34)(32,33);(8,9,13,15)(10,14,20,29)(11,23,25,16)(12,17,26,30)(18,34,35,27)(19,33,21,28)(22,37,38,31)(24,39,36,32);(8,10)(9,14)(11,24)(12,19)(13,20)(15,29)(16,32)(17,33)(18,22)(21,26)(23,39)(25,36)(27,31)(28,30)(34,37)(35,38);(9,15)(10,19,20,21)(11,25)(14,28,29,33)(17,30)(18,24,35,36)(22,38)(27,39,34,32)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26680);