Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1300 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)(8,9,14,18,13,11,15,19)(10,16,23,31,22,25,24,20)(12,17,28,32,27,26,29,33)(21,30,36,34,35,38,37,39);(8,10,13,22)(9,16,11,25)(12,21,27,35)(14,24,15,23)(17,30,26,38)(18,20,19,31)(28,37,29,36)(32,39,33,34);(8,11)(9,13)(10,20)(12,26)(14,18)(15,19)(16,24)(17,27)(21,34)(22,31)(23,25)(28,32)(29,33)(30,36)(35,39)(37,38);(8,12)(9,17)(10,21)(11,26)(13,27)(14,29)(15,28)(16,30)(18,33)(19,32)(20,34)(22,35)(23,37)(24,36)(25,38)(31,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17410);