Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C7×#60623 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
2042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17,22,24)(18,25,19,21)(20,23,28,30)(26,31,27,29);(9,12)(13,15)(16,18,21,17,22,19,25,24)(20,26,29,23,28,27,31,30);(8,10,11,14)(9,13,12,15)(16,19,21,24,22,18,25,17)(20,27,29,30,28,26,31,23);(16,20)(17,23)(18,26)(19,27)(21,29)(22,28)(24,30)(25,31);(20,28)(23,30)(26,27)(29,31)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53611);