Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#21785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2308 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1262 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)(10,20,24,15)(11,17,12,26)(13,19)(14,18)(16,25,34,27)(21,37)(22,31)(23,36,28,32)(29,35)(30,38)(33,39);(8,10)(9,15)(11,21)(12,22)(13,28)(14,24)(16,33)(17,31)(18,20)(19,36)(23,29)(25,39)(26,37)(27,38)(30,34)(32,35);(8,11,14,12)(9,16,18,34)(10,21,24,22)(13,27,29,25)(15,30,20,33)(17,19,26,35)(23,39,28,38)(31,32,37,36);(8,12,14,11)(9,17,18,26)(10,22,24,21)(13,27,29,25)(15,31,20,37)(16,19,34,35)(23,39,28,38)(30,32,33,36)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14773);