Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25199 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3019 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
990 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)(8,9,14,18,15,19,13,29)(10,20,22,16,23,33,30,34)(11,24,26,35,12,27,28,17)(21,32,38,39,25,31,37,36);(8,10,14,22,15,23,13,30)(9,16,18,33,19,34,29,20)(11,25,26,37,12,21,28,38)(17,32,24,39,35,31,27,36);(8,11,15,12)(9,17,19,35)(10,21,23,25)(13,26,14,28)(16,31,34,32)(18,27,29,24)(20,36,33,39)(22,37,30,38);(8,12,15,11)(9,17,19,35)(10,21,23,25)(13,26,14,28)(16,32,34,31)(18,24,29,27)(20,36,33,39)(22,38,30,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18187);