Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C2×C17×#3237 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
1758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(3,4)(5,11)(6,9)(7,10)(8,13)(12,17)(14,16)(15,18)(19,20,24,27)(21,28,29,34)(22,26,23,31)(25,32,33,30);(3,5,7,13)(4,8,10,11)(6,14,15,12)(9,17,18,16)(21,29)(25,33)(28,34)(30,32);(3,6,7,15)(4,9,10,18)(5,12,13,14)(8,16,11,17)(19,21)(20,25)(22,30)(23,32)(24,29)(26,34)(27,33)(28,31);(4,10)(8,11)(9,18)(16,17)(19,22,24,23)(20,26,27,31)(21,30,29,32)(25,34,33,28)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53840);