Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23818 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C22×D4 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C43×C7 ◁ G | |
758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,14)(10,15,11,13)(16,17,19,21)(18,22,23,20)(24,25,28,31)(26,29,34,38)(27,30,35,39)(32,36,33,37);(8,10,12,11)(9,13,14,15)(16,18,19,23)(17,20,21,22)(24,26)(25,29)(27,32)(28,34)(30,36)(31,38)(33,35)(37,39);(17,21)(20,22)(26,32)(27,35)(29,36)(30,39)(33,34)(37,38);(8,11,12,10)(9,13,14,15)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16806);