Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#18231 |
| 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 ◁ C23×C4×C7 ◁ G | |
1200 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(12,15)(16,17)(18,27)(19,24)(20,25)(21,30)(22,26)(23,28)(29,31);(8,9)(10,12)(11,13)(14,15)(16,18,22,19)(17,23,26,31)(20,28,21,29)(24,30,27,25);(8,10)(9,12)(11,14)(13,15)(16,19,22,18)(17,24,26,27)(20,28,21,29)(23,30,31,25);(16,20,22,21)(17,25,26,30)(18,28,19,29)(23,24,31,27)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11219);