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×#18970 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3554 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
874 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)(10,14)(11,13)(12,16)(15,19)(17,21)(18,20)(22,23)(24,25,30,35)(26,31,38,46)(27,39,41,49)(28,34,29,33)(32,43,47,40)(36,50,52,54)(37,48,42,45)(44,51,55,53);(9,13)(11,19)(14,20)(15,16)(18,23)(21,22)(24,26)(25,31)(27,36)(28,37)(29,42)(30,38)(32,44)(33,45)(34,48)(35,46)(39,54)(40,51)(41,52)(43,53)(47,55)(49,50);(8,10,12,17)(9,14,16,21)(11,18,19,23)(13,20,15,22)(24,27)(25,32)(26,36)(28,40)(29,43)(30,41)(31,44)(33,39)(34,49)(35,47)(37,51)(38,52)(42,53)(45,54)(46,55)(48,50);(10,17)(14,21)(18,23)(20,22)(24,28,30,29)(25,33,35,34)(26,37,38,42)(27,40,41,43)(31,45,46,48)(32,39,47,49)(36,51,52,53)(44,54,55,50)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11958);