Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23472 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#393 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
1148 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)(10,15)(11,23,25,34)(12,17)(13,28)(14,18)(16,26,33,27)(19,32,35,39)(20,30)(21,31)(22,37)(24,29,36,38);(8,10)(9,15)(11,24,25,36)(12,21)(13,22)(14,20)(16,32,33,39)(17,31)(18,30)(19,27,35,26)(23,38,34,29)(28,37);(8,11)(9,16)(10,19)(12,27)(13,26)(14,25)(15,29)(17,34)(18,33)(20,35)(21,24)(22,36)(23,28)(30,38)(31,39)(32,37);(10,20)(15,30)(19,35)(21,22)(24,36)(29,38)(31,37)(32,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16460);