Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×C17×AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C2×D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C23×C17 | C22×D4 |
| prime radical | C22×C17×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C22×C42×C17 ◁ G | |
3242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4,5,6);(7,8)(9,11)(10,12)(13,14);(8,11)(9,14)(12,13);(8,12)(11,13)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53144);