Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C210 |
| direct product | C7×#60387 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C2×C7 | C22×#120 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
4764 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)(10,19)(11,16)(12,18)(13,25)(14,17)(15,21)(20,35)(22,30)(23,32)(24,31)(26,29)(27,33)(28,37)(34,38)(36,39);(8,10)(9,15)(11,20)(12,21)(13,26)(14,22)(16,28)(17,29)(18,30)(19,25)(23,36)(24,38)(27,37)(31,39)(32,35)(33,34);(8,11)(9,16)(10,20)(12,23)(13,27)(14,24)(15,28)(17,31)(18,32)(19,34)(21,36)(22,38)(25,33)(26,37)(29,39)(30,35);(9,17)(15,29)(16,31)(18,25)(19,30)(28,39)(32,33)(34,35);(8,12,14,13)(9,18,17,25)(10,21,22,26)(11,23,24,27)(15,30,29,19)(16,32,31,33)(20,36,38,37)(28,35,39,34)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53375);