Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#36693 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| prime radical | C7×#392 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,14)(10,13,11,15)(16,17)(18,20)(19,21)(22,23)(24,25)(26,30)(27,31)(28,29)(32,35)(33,37)(34,36)(38,39);(8,10,12,11)(9,13,14,15)(16,18,19,23)(17,20,21,22)(25,29)(30,35)(31,36)(37,39);(9,14)(13,15)(16,17)(18,22)(19,21)(20,23)(24,26)(25,30)(27,33)(28,32)(29,35)(31,37)(34,38)(36,39);(8,11,12,10)(9,15,14,13)(17,21)(20,22)(26,32)(30,35)(33,38)(37,39);(24,27,28,34)(25,31,29,36)(26,33,32,38)(30,37,35,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29681);