Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#18306 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1040 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)(9,14)(10,18)(11,22)(15,27)(16,25)(17,23)(20,34)(21,32)(24,33)(26,29)(28,37)(30,39)(31,36)(35,38);(8,9)(10,15)(11,23)(12,17)(13,16)(14,22)(18,29)(19,28)(20,35)(21,30)(24,37)(25,33)(26,36)(27,34)(31,39)(32,38);(11,24)(14,25)(20,31)(22,33)(23,37)(26,27)(34,36)(35,39);(8,10,19,32)(9,15,28,38)(11,20,33,34)(12,21,13,18)(14,26,37,39)(16,29,17,30)(22,36,24,31)(23,35,25,27)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11294);