Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23196 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | D42 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2366 |
| prime radical | C7×#3147 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ G | |
884 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)(10,21,25,34)(11,26)(12,18)(13,19)(14,31)(15,20)(16,24,35,30)(17,27)(22,32,23,36)(28,37)(29,39,38,33);(8,10,13,30,15,25,14,24)(9,16,19,34,20,35,31,21)(11,22,12,29,28,23,27,38)(17,32,26,39,18,36,37,33);(8,11,14,27,15,28,13,12)(9,17,19,26,20,18,31,37)(10,22,24,38,25,23,30,29)(16,32,34,39,35,36,21,33);(8,12,13,28,15,27,14,11)(9,18,19,37,20,17,31,26)(10,23,24,29,25,22,30,38)(16,33,21,36,35,39,34,32)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16184);