Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C16 · Schur multiplier (H2) = C4 |
| direct product | C7×#13641 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C16 | C23 |
| commutator | C22 | C22×C7×C16 |
| Frattini, cosocle | C2×C16 | C23×C7 |
| socle | C22×C7 | C22×C16 |
| prime radical | C23×C7 | C2×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C16 ◁ G | |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 79 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,19,24,20,25,32,42,21,26,33,43,35,45,54,64,22,27,34,44,36,46,55,65,37,47,56,66,57,67,72,77)(18,23,29,39,30,40,51,61,31,41,52,62,53,63,71,76,28,38,48,58,49,59,68,73,50,60,69,74,70,75,78,79);(9,12)(13,15)(16,18)(17,23)(19,29)(20,30)(21,31)(22,28)(24,39)(25,40)(26,41)(27,38)(32,51)(33,52)(34,48)(35,53)(36,49)(37,50)(42,61)(43,62)(44,58)(45,63)(46,59)(47,60)(54,71)(55,68)(56,69)(57,70)(64,76)(65,73)(66,74)(67,75)(72,78)(77,79);(8,10,11,14)(9,13,12,15)(18,28)(23,38)(29,48)(30,49)(31,50)(39,58)(40,59)(41,60)(51,68)(52,69)(53,70)(61,73)(62,74)(63,75)(71,78)(76,79)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6629);