Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17×C32 · Schur multiplier (H2) = C2 |
| direct product | C17×#7510 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C17×C32 | C22 |
| commutator | C2 | C4×C17×C32 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| socle, prime radical | C22×C17 | C2×C32 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17×C32 ◁ G | |
82 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)(22,23,24,30,25,31,34,48,26,32,35,49,38,51,54,70,27,33,36,50,39,52,55,71,41,53,57,72,60,73,74,83,28,29,37,44,40,45,56,64,42,46,58,65,61,67,75,79,43,47,59,66,62,68,76,80,63,69,77,81,78,82,84,85);(18,19,20,21)(23,29)(30,44)(31,45)(32,46)(33,47)(48,64)(49,65)(50,66)(51,67)(52,68)(53,69)(70,79)(71,80)(72,81)(73,82)(83,85)2720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 498);