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×#18972 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
818 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)(9,13)(11,18)(14,20)(15,19)(17,22)(21,23)(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);(8,9,12,15)(10,14,16,21)(11,19,18,13)(17,23,22,20)(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);(8,10,12,16)(9,14,15,21)(11,17,18,22)(13,20,19,23)(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);(10,16)(14,21)(17,22)(20,23)(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, 11960);