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×#7546 |
| 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 | |
66 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)(24,35)(25,36)(26,40)(27,43)(30,39)(31,54)(32,58)(33,61)(34,49)(37,68)(38,53)(41,72)(42,67)(44,71)(45,46)(47,55)(48,59)(50,75)(51,52)(56,84)(57,79)(60,78)(62,63)(64,69)(65,66)(70,81)(73,82)(74,80)(76,85)(77,83);(22,23,30,50,25,31,51,78,40,55,81,84,66,74,69,61,27,33,53,80,41,56,37,47,44,60,63,54,67,75,24,29,28,34,35,46,42,57,62,58,71,83,68,82,72,85,38,48,43,59,64,76,65,73,70,77,26,32,52,79,36,45,39,49)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 534);