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C59×#365 #16836899

order3776
nilpotency class4
isoclinismisoclinic class of #365
automorphism?
homologyAbelianization (H1) = C2×C4×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×#365

Subgroups

subgroupG/H
center, socleC2×C59#106
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

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 75
transitive degreeμt(G) = 944

A minimal faithful permutation representation — 2 generators on 75 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)(61,65,66,71)(62,68)(63,70)(67,74,73,72)(69,75);(60,61,62,65,63,67,68,72,64,66,69,71,70,73,75,74)

Conjugacy classes & character table

944 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C59×#365, C59×#2155, C59×#2180, …
maximal normal subgroup ofC2×C59×#365, C59×#2155, C59×#2180, …
maximal quotient ofC59×#1368, C59×#1383, C2×C59×#365

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 46);