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C59×#453 #16836987

order3776
nilpotency class3
isoclinismisoclinic class of #453
automorphism?
homologyAbelianization (H1) = C23×C59 · Schur multiplier (H2) = C23

Aliases

direct productC59×#453

Subgroups

subgroupG/H
center, socleC2×C59#120
commutator, Frattini, cosocleC2×C4C23×C59
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C59 ◁ C2×C4×C59 ◁ G

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 472

A minimal faithful permutation representation — 3 generators on 67 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)(61,64)(62,66)(65,67);(60,61)(62,67)(63,65)(64,66);(62,66)(64,67)

Conjugacy classes & character table

944 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC59×#1402, C59×#2196, C59×#2198, …
maximal normal subgroup ofC59×#1402, C59×#2196, C59×#2198, …
maximal quotient ofC59×#1595, C59×#1596, C59×#1600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 134);