Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C210 |
| direct product | C2×C17×#2901 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C22×C22⋊C4 |
| prime radical | C2×C17×#585 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×#41×C17 ◁ G | |
4946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4,7,11,8,5,12,10)(6,9,15,17,14,13,18,16);(3,5)(4,8)(6,13)(7,10)(9,14)(11,12)(15,16)(17,18);(3,6)(4,9)(5,13)(7,15)(8,14)(10,16)(11,17)(12,18);(6,14)(9,13)(15,18)(16,17)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53080);