Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#18426 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
1168 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(9,13)(10,11)(14,15)(16,17)(18,22)(19,21)(20,24)(23,27)(25,29)(26,28)(30,31);(8,9)(10,13)(11,15)(12,14)(17,21)(19,27)(22,28)(23,24)(26,31)(29,30);(10,11)(13,15)(16,18)(17,22)(19,26)(20,25)(21,28)(23,30)(24,29)(27,31);(8,10,12,11)(9,13,14,15)(18,25)(22,29)(26,31)(28,30)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11414);