Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#21777 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2308 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| prime radical | C7×#3485 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C24×C7 ◁ G | |
1318 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)(10,18,21,14)(11,15)(12,24,25,16)(13,17)(19,26,33,28)(20,27)(22,35,36,29)(23,30)(31,34)(32,38)(37,39);(8,10)(9,14)(11,19)(12,20)(13,21)(15,28)(16,27)(17,18)(22,32)(23,33)(24,31)(25,34)(26,30)(29,38)(35,37)(36,39);(8,11,13,23)(9,15,17,30)(10,19,21,33)(12,22,25,36)(14,26,18,28)(16,29,24,35)(20,32,34,39)(27,37,31,38);(8,12)(9,16)(10,20)(11,22)(13,25)(14,27)(15,29)(17,24)(18,31)(19,32)(21,34)(23,36)(26,37)(28,38)(30,35)(33,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14765);