Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18290 |
| 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 ◁ C23×C4×C7 ◁ G | |
1034 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)(11,21)(15,27)(16,25)(17,22)(19,33)(20,32)(23,36)(26,28)(29,39)(30,37)(31,35)(34,38);(8,9)(10,15)(11,22)(12,17)(13,16)(14,21)(18,28)(19,34)(20,29)(23,37)(24,30)(25,36)(26,35)(27,33)(31,39)(32,38);(11,23)(14,25)(19,31)(21,36)(22,37)(26,27)(33,35)(34,39);(8,10,12,20)(9,15,17,29)(11,19,21,35)(13,18,24,32)(14,26,22,34)(16,28,30,38)(23,31,36,33)(25,27,37,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11278);