Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #34980 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#35101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
1622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,11,14,13)(16,17,19,21)(18,20,22,23)(27,34)(31,36)(33,38)(37,39);(8,10,12,14)(9,13,15,11)(16,17)(18,20)(19,21)(22,23)(25,29)(26,32)(31,36)(33,38);(8,9)(10,13)(11,14)(12,15)(24,25,28,29)(26,30,32,35)(27,31,34,36)(33,37,38,39);(24,26)(25,30)(27,33)(28,32)(29,35)(31,37)(34,38)(36,39);(8,11,12,13)(9,14,15,10)(16,18,19,22)(17,20,21,23)(24,27)(25,31)(26,33)(28,34)(29,36)(30,37)(32,38)(35,39)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 28089);