Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23391 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#23746 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
814 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)(18,20)(19,21)(22,23)(24,25)(26,32)(27,29)(28,31)(30,34)(33,38)(35,37)(36,39);(8,10,12,11)(9,13,14,15)(16,18,19,22)(17,20,21,23)(25,29)(26,33)(28,35)(30,38)(32,39)(34,36);(8,11,12,10)(9,13,14,15)(17,21)(20,23)(24,26,27,34)(25,30,29,32)(28,36,35,33)(31,38,37,39);(26,34)(30,32)(33,36)(38,39)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16734);