Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13400 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C7×#3060 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,19)(11,25)(12,17)(13,31)(14,18)(15,22)(16,29)(20,27)(21,36)(23,37)(24,33)(26,28)(30,39)(32,38)(34,35);(8,9)(10,20)(11,26)(12,31)(13,17)(14,18)(15,23)(16,30)(19,35)(21,34)(22,33)(24,32)(25,28)(27,36)(29,39)(37,38);(8,10,13,23,14,21,12,24)(9,15,17,34,18,32,31,20)(11,27,29,38,30,35,28,22)(16,33,25,36,26,37,39,19)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6388);