Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C17×#332 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C22⋊C4 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle, prime radical | C23×C17 | C2×C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C43×C17 ◁ G | |
540 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(6,9)(7,11)(10,12)(13,14,16,18,17,20,15,19);(5,6,8,10)(7,12,11,9)(14,18)(15,16)(19,20)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1218);