C₂₉×#3559 #16817273

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3559

Subgroups

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

1024 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)(31,34)(32,36)(38,39)(40,47)(41,44)(42,50)(43,46)(45,51)(48,52)(49,53);(31,34)(35,37)(38,40,43,41)(39,44,46,47)(42,48,51,49)(45,52,50,53);(30,31)(32,35)(33,34)(36,37)(38,41,43,40)(39,44,46,47)(42,49,51,48)(45,52,50,53);(30,32,33,36)(31,35,34,37)(38,39)(40,47)(41,44)(42,45)(43,46)(48,53)(49,52)(50,51);(38,42)(39,45)(40,48)(41,49)(43,51)(44,52)(46,50)(47,53)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8486, C₂₉×#8513, C₂₉×#18244, …
maximal normal subgroup of	C₂₉×#8486, C₂₉×#8513, C₂₉×#18244, …
maximal quotient of	C₂₉×#34378, C₂₉×#34382, C₂₉×#34398, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2291);

C29×#3559 #16817273