Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11184 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23)(24,34)(25,39,43,48)(26,32)(27,31)(28,33)(29,36)(30,41,49,42)(35,44,52,53)(37,46)(38,45)(40,50,51,47);(18,19)(20,21)(22,24,28,38)(23,29,33,46)(25,40,43,51)(26,37,27,36)(30,47,49,50)(31,45,32,34)(35,41,52,42)(39,44,48,53);(19,21)(22,25,26,41,28,43,27,42)(23,30,31,48,33,49,32,39)(24,35,36,51,38,52,37,40)(29,44,34,50,46,53,45,47)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4172);