Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24409 |
| 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 | |
1336 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)(10,18,21,14)(11,22)(12,16)(13,17)(15,24)(19,36,37,29)(20,34,27,30)(23,39,38,31)(25,35)(26,33)(28,32);(8,10)(9,14)(11,23)(12,21)(13,27)(15,31)(16,18)(17,34)(19,25)(20,26)(22,39)(24,38)(28,37)(29,32)(30,33)(35,36);(8,11)(9,15)(10,19)(12,24)(13,28)(14,29)(16,22)(17,35)(18,36)(20,38)(21,37)(23,27)(25,26)(30,39)(31,34)(32,33);(8,10)(9,14)(11,19)(12,21)(13,20)(15,29)(16,18)(17,30)(22,36)(23,25)(24,37)(26,27)(28,38)(31,32)(33,34)(35,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17397);