Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×C7×#1477 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C2×D4 |
| commutator | C4 | C23×C7×C8 |
| Frattini, cosocle | C42 | C24×C7 |
| socle | C23×C7 | C2×C22⋊C4 |
| prime radical | C22×C7×#41 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C22×C42×C7 ◁ G | |
1370 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(4,7)(5,9)(8,10)(11,12,13,15,14,16,17,18);(3,4)(5,10)(6,8)(7,9);(4,8)(7,10)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10424);