Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13401 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| socle | C2×C7 | #2034 |
| prime radical | C7×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 71 points:
(1,2,3,4,5,6,7)(8,9)(10,20)(11,26)(12,31)(13,35)(14,19)(15,22)(16,29)(17,34)(18,33)(21,49)(23,39)(24,40)(25,41)(27,60)(28,62)(30,59)(32,45)(36,44)(37,58)(38,54)(42,65)(43,64)(46,63)(47,51)(48,55)(50,71)(52,57)(53,66)(56,70)(61,68)(67,69);(8,10)(9,15)(11,27)(12,24)(13,23)(14,25)(16,38)(17,41)(18,39)(19,40)(20,31)(21,30)(22,34)(26,57)(28,50)(29,61)(32,52)(33,55)(35,66)(36,67)(37,56)(42,47)(43,69)(44,68)(45,49)(46,70)(48,58)(51,64)(53,63)(54,65)(59,71)(60,62);(8,11,14,30)(9,16,19,43)(10,21)(12,32,34,28)(13,36,37,65)(15,38)(17,44,31,42)(18,45,46,62)(20,47)(22,52)(23,54)(24,50)(25,27)(26,58,59,35)(29,63,64,33)(39,49)(40,69)(41,68)(48,71)(51,55)(53,61)(56,67)(57,66)(60,70)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6389);