Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7540 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#7540 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1415 |
| commutator | C32 | C2×C4×C17 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| prime radical | C17×#2262 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ C2×C17×C32 ◁ G | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,25,26,47)(20,30)(21,36)(22,38)(23,42)(27,53,51,61)(28,55,52,60)(29,56,44,50)(31,37,48,46)(32,40)(33,65)(34,69)(35,45)(39,64)(41,49,77,79)(43,75)(54,66,73,81)(57,58)(59,67)(62,76,70,74)(63,78)(68,80)(71,72);(18,19)(20,31)(21,37)(22,41)(23,44)(24,26)(25,45)(27,36)(28,38)(29,42)(30,47)(32,51)(33,66)(34,70)(35,48)(39,76)(40,46)(43,77)(49,80)(50,59)(52,75)(53,78)(54,64)(55,63)(56,69)(57,61)(58,60)(62,67)(65,79)(68,81)(71,74)(72,73)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 528);