Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24001 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3020 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1122 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)(10,15)(11,22)(12,17)(13,28)(14,19)(16,26)(18,31)(20,36)(21,27)(23,39)(24,38)(25,35)(29,33)(30,34)(32,37);(8,10,14,17)(9,15,19,12)(11,23)(13,21,31,34)(16,32)(18,30,28,27)(20,25)(22,36)(24,33)(26,38)(29,37)(35,39);(8,11)(9,16)(10,20)(12,24)(13,29)(14,25)(15,32)(17,23)(18,35)(19,33)(21,38)(22,28)(26,31)(27,36)(30,39)(34,37);(8,12,14,15)(9,17,19,10)(11,24,25,32)(13,30,31,27)(16,23,33,20)(18,21,28,34)(22,37,35,38)(26,36,29,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16989);