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) = C2 |
| direct product | C17×#7538 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | D32 |
| commutator | C32 | C2×C4×C17 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| 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 | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 4352 |
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)(23,29)(24,34)(25,36)(26,41)(27,45)(30,52)(31,56)(32,59)(33,51)(35,40)(37,67)(38,71)(39,48)(42,76)(43,53)(44,49)(46,57)(47,50)(54,84)(55,83)(58,85)(60,61)(62,69)(63,77)(64,75)(65,66)(68,73)(70,81)(72,74)(78,82)(79,80);(22,23,28,33)(24,35,39,64)(25,40,43,75)(26,44,46,78)(27,47,45,32)(29,48,51,34)(30,53,55,36)(31,57,58,41)(37,68,70,84)(38,72,69,63)(42,77,65,74)(49,81,82,67)(50,62,59,71)(52,79,83,60)(54,66,73,76)(56,80,85,61)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 526);