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×#15139 |
| 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 | |
1250 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)(9,11)(16,17,21,19)(18,23,20,22)(26,31)(27,29);(13,15)(16,18,21,20)(17,22,19,23)(24,25,28,30)(26,29,31,27);(12,13)(14,15)(16,19,21,17)(18,23,20,22)(24,26)(25,29)(27,30)(28,31);(8,9,10,11)(16,20,21,18)(17,23,19,22)(24,27,28,29)(25,26,30,31)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 8127);