Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C4×C17×#533 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C17 | C23 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| prime radical | C24×C17 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C17 ◁ G | |
2550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 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);(5,6)(7,10)(8,9)(11,12)(13,14,16,18)(15,19,20,17);(6,9)(10,12);(13,15,16,20)(14,17,18,19);(5,7,8,11)(6,10,9,12)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27027);