C₂₉×#3509 #16817223

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3509

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 5 generators on 53 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)(32,36)(34,37)(38,39,42,45)(40,43,48,46)(41,49,50,44)(47,52,53,51);(30,31,33,35)(32,34,36,37)(38,39)(40,46)(41,44)(42,45)(43,48)(47,52)(49,50)(51,53);(30,32,33,36)(31,34,35,37);(38,40)(39,43)(41,47)(42,48)(44,51)(45,46)(49,52)(50,53);(38,41,42,50)(39,44,45,49)(40,47,48,53)(43,51,46,52)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8427, C₂₉×#8474, C₂₉×#12724, …
maximal normal subgroup of	C₂₉×#8427, C₂₉×#8474, C₂₉×#12724, …
maximal quotient of	C₂₉×#34188, C₂₉×#34209, C₂₉×#34214, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2241);

C29×#3509 #16817223