Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61324 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3038 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×Q8×C17 ◁ G | |
1878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,24)(26,27,31,35)(28,32,30,34)(29,37,38,40)(33,39,41,36);(18,19,21,22)(20,24,25,23)(26,28,31,30)(27,32,35,34)(29,36,38,39)(33,40,41,37);(26,29)(27,33)(28,36)(30,39)(31,38)(32,40)(34,37)(35,41);(18,20,21,25)(19,23,22,24);(26,28,31,30)(27,34,35,32)(29,36,38,39)(33,37,41,40)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54312);