Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of AΣL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×C7×#1326 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #99 |
| commutator | C23 | C22×C7×C8 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C7 |
| prime radical | C25×C7 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C24×C7 ◁ C22×C7×C22⋊C4 ◁ G | |
770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4,5,7,6,8,9,10)(11,12)(13,17,18,15)(14,16);(12,15,16,17)(13,18)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4439);