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×#7545 |
| 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)(24,30)(25,35)(26,39)(27,42)(31,53)(32,57)(33,60)(34,48)(36,64)(37,67)(38,52)(40,69)(41,63)(43,68)(44,45)(46,54)(47,58)(49,50)(51,65)(55,82)(56,80)(59,83)(61,62)(66,85)(70,79)(71,78)(72,74)(73,84)(75,81)(76,77);(22,23,30,45,25,31,49,57,39,54,64,79,62,71,37,47,27,33,51,73,40,55,66,75,43,59,77,80,63,72,38,48,28,34,52,74,41,56,76,83,68,81,85,82,69,84,65,60,42,58,67,78,61,70,36,46,26,32,50,53,35,44,24,29)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 533);