Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#15186 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(12,13)(14,15)(16,17,19,21)(18,22,23,20)(24,25,28,31)(26,30,27,29);(9,11)(13,14)(16,17,19,21)(18,20,23,22)(24,25)(26,29)(27,30)(28,31);(8,9)(10,11)(12,14,15,13)(16,17)(18,20)(19,21)(22,23)(24,26,28,27)(25,29,31,30);(16,18,19,23)(17,20,21,22)(24,27,28,26)(25,30,31,29)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 8174);