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×#18287 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C25×C7 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1064 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)(8,9,12,17)(10,18,21,31)(11,22,25,16)(13,15,26,30)(14,23,28,19)(20,32,34,39)(24,35,37,29)(27,36,38,33);(8,10,12,21)(9,14,17,28)(11,23,25,19)(13,20,26,34)(15,27,30,38)(16,31,22,18)(24,36,37,33)(29,39,35,32);(11,24)(16,29)(18,32)(19,33)(22,35)(23,36)(25,37)(31,39);(9,15)(14,27)(16,29)(17,30)(18,32)(22,35)(28,38)(31,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11275);