Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1324 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)(8,9,13,20,15,21,14,19)(10,22,26,35,27,37,25,16)(11,28,31,18,12,32,30,17)(23,33,29,36,38,39,24,34);(8,10)(9,16)(11,29)(12,24)(13,26)(14,25)(15,27)(17,36)(18,34)(19,37)(20,22)(21,35)(23,30)(28,39)(31,38)(32,33);(8,11,15,12)(9,17,21,18)(10,23,27,38)(13,30,14,31)(16,33,35,39)(19,28,20,32)(22,34,37,36)(24,25,29,26);(8,12,15,11)(9,18,21,17)(10,24,27,29)(13,30,14,31)(16,34,35,36)(19,28,20,32)(22,33,37,39)(23,25,38,26)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17463);