Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C214 |
| direct product | C23×C7×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C7 | C23 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C7 ◁ G | |
12190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 6 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4);(5,6);(8,10)(11,12,15,18)(13,17,14,16);(11,13,15,14)(12,16,18,17);(7,8,9,10)(11,14,15,13)(12,17,18,16)784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55653);