Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C2×C7×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
1622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 55 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,14)(12,15)(13,18)(17,22)(19,21)(20,23)(24,25,29,34)(26,30,35,43)(27,32,38,46)(28,31,40,33)(36,42,48,53)(37,44,49,41)(39,45,51,47)(50,54,55,52);(8,10,12,18)(9,13,15,16)(11,19,20,17)(14,22,23,21)(24,26)(25,30)(27,36)(28,37)(29,35)(31,44)(32,42)(33,41)(34,43)(38,48)(39,50)(40,49)(45,54)(46,53)(47,52)(51,55);(8,11,12,20)(9,14,15,23)(10,17,18,19)(13,21,16,22)(25,31)(26,35)(28,40)(30,41)(32,45)(33,34)(36,48)(39,51)(42,52)(43,44)(46,47)(53,54);(9,15)(13,16)(14,23)(21,22)(24,27)(25,32)(26,36)(28,39)(29,38)(30,42)(31,45)(33,47)(34,46)(35,48)(37,50)(40,51)(41,52)(43,53)(44,54)(49,55);(27,38)(32,46)(36,48)(39,51)(42,53)(45,47)(50,55)(52,54)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53872);