Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#33856 |
| 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 | |
652 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)(11,24)(12,13)(16,17)(18,34)(19,33)(21,37)(22,38)(23,29)(25,30)(27,28)(31,32)(35,36);(8,9)(10,21)(11,25)(12,18)(13,30)(14,19)(15,24)(16,23)(17,22)(20,35)(26,36)(27,33)(28,34)(29,32)(31,39)(37,38);(8,10)(9,16)(11,22)(12,29)(13,20)(14,23)(15,31)(17,34)(18,35)(19,21)(24,26)(25,37)(27,39)(28,38)(30,32)(33,36);(8,10)(9,17)(11,26)(12,20)(13,29)(14,23)(15,32)(16,34)(18,36)(19,37)(21,25)(22,24)(27,38)(28,39)(30,31)(33,35)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26844);