C₂₉×#3502 #16817216

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

Aliases

direct product

C₂₉×#3502

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
prime radical	C₂³×C₂₉	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

964 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)(30,31,33,35)(32,36,37,34)(38,39,43,47)(40,45,41,44)(42,46,50,53)(48,52,49,51);(38,40,43,41)(39,44,47,45)(42,49,50,48)(46,52,53,51);(30,32,33,37)(31,34,35,36)(38,41,43,40)(39,45,47,44)(42,49,50,48)(46,52,53,51);(38,42,43,50)(39,46,47,53)(40,48,41,49)(44,51,45,52);(38,39)(40,44)(41,45)(42,46)(43,47)(48,51)(49,52)(50,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8356, C₂₉×#8433, C₂₉×#8460, …
maximal normal subgroup of	C₂₉×#8356, C₂₉×#8433, C₂₉×#8460, …
maximal quotient of	C₂₉×#34182, C₂₉×#34213, C₂₉×#34249, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2234);

C29×#3502 #16817216