Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61629 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61866 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#121 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#533 ◁ G | |
1606 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)(24,25,29,33)(26,30,35,44)(27,37,39,47)(28,40,42,32)(31,41,46,38)(34,48,49,55)(36,52,51,45)(43,53,54,50);(8,10,12,18)(9,13,15,16)(11,19,20,17)(14,22,23,21)(24,26)(25,30)(27,34)(28,36)(29,35)(31,43)(32,45)(33,44)(37,48)(38,50)(39,49)(40,52)(41,53)(42,51)(46,54)(47,55);(24,27,29,39)(25,31,33,46)(26,34,35,49)(28,41,42,38)(30,43,44,54)(32,47,40,37)(36,53,51,50)(45,55,52,48);(8,11,12,20)(9,14,15,23)(10,17,18,19)(13,21,16,22)(26,35)(30,44)(34,49)(36,51)(43,54)(45,52)(48,55)(50,53);(9,15)(13,16)(14,23)(21,22)(26,35)(30,44)(34,49)(36,51)(43,54)(45,52)(48,55)(50,53)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54854);