Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18323 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3459 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1008 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)(8,9,13,18)(10,20,23,35)(11,17,12,26)(14,19,30,36)(15,27,33,21)(16,25,28,29)(22,38,24,31)(32,37,34,39);(8,10)(9,15)(11,21)(12,27)(13,23)(14,24)(16,31)(17,35)(18,33)(19,34)(20,26)(22,30)(25,37)(28,38)(29,39)(32,36);(8,9)(10,15)(11,16)(12,28)(13,18)(14,19)(17,29)(20,37)(21,31)(22,32)(23,33)(24,34)(25,26)(27,38)(30,36)(35,39);(8,11,13,12)(9,16,18,28)(10,21,23,27)(14,25,30,29)(15,31,33,38)(17,19,26,36)(20,32,35,34)(22,39,24,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11311);