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×#24421 |
| 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 | |
1310 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)(8,9,14,28,13,15,12,18)(10,19,27,16,22,30,20,29)(11,23,25,32,26,17,24,33)(21,34,35,38,36,39,37,31);(9,15)(10,20)(12,14)(16,30)(17,23)(19,29)(21,35)(22,27)(24,25)(31,39)(34,38)(36,37);(8,10)(9,16)(11,21)(12,27)(13,22)(14,20)(15,29)(17,31)(18,30)(19,28)(23,38)(24,35)(25,37)(26,36)(32,34)(33,39);(8,11)(9,17)(10,21)(12,25)(13,26)(14,24)(15,23)(16,31)(18,33)(19,34)(20,35)(22,36)(27,37)(28,32)(29,38)(30,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17409);