Finite Group Databasebeta

C59×#362 #16836896

order3776
nilpotency class4
isoclinismisoclinic class of #360
automorphism?
homologyAbelianization (H1) = C2×C4×C59 · Schur multiplier (H2) = C2

Aliases

direct productC59×#362

Subgroups

subgroupG/H
center, socleC2×C59#102
commutatorC8C2×C4×C59
Frattini, cosocleC2×C8C22×C59
prime radicalC22×C59SD16
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ C2×C4×C59 ◁ C2×C8×C59 ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(60,61,64,68,65,70,80,69)(62,71,73,84,74,88,79,87)(63,75,77,67,78,85,91,86)(66,76,81,72,83,89,82,90);(60,62,65,74)(61,66,70,83)(63,76,78,89)(64,79,80,73)(67,84,86,87)(68,82,69,81)(71,75,88,85)(72,77,90,91)

Conjugacy classes & character table

944 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C59×#362, C59×#2148, C59×#2180, …
maximal normal subgroup ofC2×C59×#362, C59×#2148, C59×#2180, …
maximal quotient ofC59×#1334, C59×#1350, C59×#1362, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 43);