Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18331 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3460 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
998 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)(8,9,14,20)(10,22,24,35)(11,18,12,28)(13,19,15,21)(16,29,33,23)(17,27,30,26)(25,32,31,39)(34,38,36,37);(8,10)(9,16)(11,23)(12,29)(13,31)(14,24)(15,25)(17,32)(18,35)(19,36)(20,33)(21,34)(22,28)(26,38)(27,37)(30,39);(8,9,15,21)(10,16,25,34)(11,17,27,28)(12,30,26,18)(13,19,14,20)(22,23,32,37)(24,33,31,36)(29,39,38,35);(8,11,14,12)(9,17,20,30)(10,23,24,29)(13,26,15,27)(16,32,33,39)(18,21,28,19)(22,36,35,34)(25,37,31,38)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11319);