Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23474 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #393 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| socle | C2×C7 | C2×#393 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
1164 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)(10,14)(11,21,24,15)(12,16)(13,17)(18,31,22,26)(19,27)(20,28)(23,34,36,29)(25,30)(32,39,35,37)(33,38);(8,10)(9,14)(11,22,24,18)(12,19)(13,20)(15,26,21,31)(16,27)(17,28)(23,35,36,32)(25,33)(29,37,34,39)(30,38);(8,11)(9,15)(10,18)(12,23)(13,24)(14,26)(16,29)(17,21)(19,32)(20,22)(25,36)(27,37)(28,31)(30,34)(33,35)(38,39);(8,12,13,25)(9,16,17,30)(10,19,20,33)(11,23,24,36)(14,27,28,38)(15,29,21,34)(18,32,22,35)(26,37,31,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16462);