Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C17×#367 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | D8 |
| commutator | C8 | C2×C42×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle, prime radical | C23×C17 | C2×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
366 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(5,6,7,8)(10,14)(11,18)(12,19)(15,20)(16,24)(17,23)(21,22);(9,10,15,24,12,16,11,14,13,17,18,22,19,21,20,23)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5661);