Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#26925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C23×C7 | H(5,𝔽2) |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,12)(10,14,15,13)(16,17,21,26,23,19,22,27)(18,28,31,34,33,29,32,24)(20,36,37,35,39,41,38,25)(30,40,44,43,46,47,45,42);(9,12)(13,14)(16,18,23,33)(17,24,19,34)(20,30,39,46)(21,32,22,31)(25,40,35,47)(26,29,27,28)(36,42,41,43)(37,45,38,44);(16,19,23,17)(18,29,33,28)(20,35,39,25)(21,26,22,27)(24,31,34,32)(30,43,46,42)(36,38,41,37)(40,45,47,44);(8,10,11,15)(9,13,12,14)(16,20)(17,25)(18,30)(19,35)(21,38)(22,37)(23,39)(24,40)(26,41)(27,36)(28,42)(29,43)(31,45)(32,44)(33,46)(34,47)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19913);