Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#19003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
808 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7)(10,16)(11,18)(13,21)(14,19)(17,20)(22,23)(24,25)(26,36)(27,40)(28,35)(29,34)(30,33)(31,38)(32,41)(37,45)(39,48)(42,49)(43,46)(44,47)(50,52)(51,54)(53,55);(8,9,12,15)(10,13,17,22)(11,19,18,14)(16,23,20,21)(24,26)(25,31)(27,37)(28,43)(29,38)(30,39)(32,45)(33,46)(34,48)(35,36)(40,54)(41,52)(42,53)(44,51)(47,55)(49,50);(8,10)(9,13)(11,20)(12,17)(14,23)(15,22)(16,18)(19,21)(24,27,30,42)(25,32,33,47)(26,37,39,53)(28,41,29,44)(31,45,46,55)(34,40,35,49)(36,50,48,54)(38,51,43,52);(25,33)(31,46)(32,47)(34,35)(36,48)(40,49)(45,55)(50,54)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11991);