Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60388 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C210 |
| direct product | C7×#60391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C22×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C7×#41 ◁ G | |
4666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,14,11)(10,18,22,31)(12,16,25,23)(13,24,28,17)(15,27,19,21)(20,32,34,39)(26,36,37,30)(29,38,33,35);(8,10)(9,15)(11,19)(12,20)(13,27)(14,22)(16,29)(17,31)(18,24)(21,28)(23,33)(25,34)(26,38)(30,39)(32,36)(35,37);(8,11,14,9)(10,19,22,15)(12,23,25,16)(13,17,28,24)(18,27,31,21)(20,33,34,29)(26,30,37,36)(32,38,39,35);(8,12)(9,16)(10,20)(11,23)(13,26)(14,25)(15,29)(17,30)(18,32)(19,33)(21,35)(22,34)(24,36)(27,38)(28,37)(31,39);(12,25)(16,23)(20,34)(26,37)(29,33)(30,36)(32,39)(35,38)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53379);