Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#7179 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | D8 |
| commutator | C8 | C4×C8×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| socle | C22×C17 | D4⋊C8 |
| prime radical | C23×C17 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C22×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
274 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,25,31,27,32,34,30,28,33,24,29,26,36,35,37);(19,21)(23,29,32,37,33,31,36,30)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 167);