Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#7537 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D32 |
| commutator | C32 | C2×C4×C17 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| prime radical | C2×C17×D32 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ C2×C17×C32 ◁ G | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 2 generators on 85 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23)(24,29)(25,40)(26,44)(27,47)(28,34)(30,35)(31,36)(32,41)(33,45)(37,57)(38,59)(39,51)(42,75)(43,73)(46,77)(48,61)(49,60)(50,68)(52,67)(53,70)(54,63)(55,76)(56,66)(58,74)(62,78)(64,72)(65,71)(69,82)(79,85)(80,84)(81,83);(23,29)(24,35)(25,36)(26,41)(27,45)(30,31)(32,57)(33,59)(34,51)(37,67)(38,70)(39,63)(40,48)(42,76)(43,66)(44,49)(46,74)(47,50)(52,72)(53,71)(54,56)(55,78)(58,82)(60,61)(62,68)(64,65)(69,85)(73,80)(75,79)(77,81)(83,84)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 525);