Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33854 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#33854 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C7×#443 ◁ G | |
656 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(9,15)(10,20)(11,23)(12,13)(16,33)(17,35)(18,37)(19,32)(21,38)(22,28)(24,29)(26,27)(30,34)(31,36);(8,9)(10,16)(11,24)(12,18)(13,29)(14,19)(15,23)(17,21)(20,34)(22,35)(25,30)(26,32)(27,37)(28,31)(33,38)(36,39);(8,10)(9,16)(11,21)(12,28)(13,20)(14,22)(15,30)(17,24)(18,31)(19,35)(23,25)(26,39)(27,38)(29,34)(32,36)(33,37);(8,10)(9,17)(11,25)(12,20)(13,28)(14,22)(15,31)(16,24)(18,30)(19,33)(21,23)(26,38)(27,39)(29,36)(32,34)(35,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26842);