Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23995 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24288 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2408 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ G | |
1290 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)(10,22)(11,27)(12,30)(13,20)(14,19)(15,21)(16,25)(17,29)(18,31)(23,34)(24,39)(26,38)(28,35)(32,37)(33,36);(8,10,13,25,15,26,14,28)(9,16,19,22,21,35,20,38)(11,23,29,12,24,31,33,32)(17,18,27,30,36,34,39,37);(8,11)(9,17)(10,23)(12,25)(13,29)(14,33)(15,24)(16,34)(18,35)(19,27)(20,39)(21,36)(22,37)(26,31)(28,32)(30,38);(8,12,13,31,15,32,14,23)(9,18,19,30,21,34,20,37)(10,24,25,33,26,11,28,29)(16,27,22,36,35,39,38,17)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17276);