Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18953 |
| 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 | |
846 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)(8,9,14,18)(10,19,11,16)(12,17,13,22)(15,21,23,20)(24,25)(26,30)(27,37)(28,40)(29,32)(31,39)(33,43)(34,50)(35,48)(36,45)(38,49)(41,46)(42,47)(44,52)(51,54)(53,55);(8,10,14,11)(9,15,18,23)(12,20,13,21)(16,22,19,17)(24,26,29,36)(25,30,32,45)(27,34,38,51)(28,41,43,35)(31,44,47,55)(33,48,40,46)(37,54,49,50)(39,53,42,52);(8,11,14,10)(9,16,18,19)(12,20,13,21)(15,22,23,17)(24,27)(25,31)(26,34)(28,42)(29,38)(30,44)(32,47)(33,49)(35,53)(36,51)(37,40)(39,43)(41,52)(45,55)(46,54)(48,50);(8,12,14,13)(9,17,18,22)(10,20,11,21)(15,16,23,19)(25,32)(30,45)(31,47)(33,40)(37,49)(44,55)(46,48)(50,54)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11941);