Finite Group Databasebeta

C59×#578 #16837112

order3776
nilpotency class3
isoclinismisoclinic class of #576
automorphism?
homologyAbelianization (H1) = C24×C59 · Schur multiplier (H2) = C25

Aliases

direct productC59×#578

Subgroups

subgroupG/H
center, socleC2×C59C22×D4
commutator, Frattini, cosocleC4C24×C59
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ #41×C59 ◁ G

248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 91
transitive degreeμt(G) = 1888

A minimal faithful permutation representation — 4 generators on 91 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59)(60,61,65,69)(62,70,73,83)(63,67,74,81)(64,76,78,68)(66,77,80,72)(71,84,85,91)(75,88,87,82)(79,89,90,86);(60,62,65,73)(61,66,69,80)(63,71,74,85)(64,77,78,72)(67,79,81,90)(68,83,76,70)(75,89,87,86)(82,91,88,84);(60,63)(61,67)(62,71)(64,75)(65,74)(66,79)(68,82)(69,81)(70,84)(72,86)(73,85)(76,88)(77,89)(78,87)(80,90)(83,91);(63,74)(67,81)(71,85)(75,87)(79,90)(82,88)(84,91)(86,89)

Conjugacy classes & character table

1298 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC59×#2193, C59×#2195, C59×#3289, …
maximal normal subgroup ofC59×#2193, C59×#2195, C59×#3289, …
maximal quotient ofC59×#2898, C59×#2913, C59×#2947, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 259);