C₂₉×#3504 #16817218

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

Aliases

direct product

C₂₉×#3504

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

988 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)(40,44)(41,48)(42,43)(45,49)(46,52)(47,50)(51,53);(39,43)(44,50)(45,48)(51,52);(30,32,33,37)(31,34,35,36)(38,40,42,47)(39,44,43,50)(41,46,49,53)(45,51,48,52);(38,39)(40,44)(41,45)(42,43)(46,51)(47,50)(48,49)(52,53);(38,41,42,49)(39,45,43,48)(40,46,47,53)(44,51,50,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8478, C₂₉×#17689, C₂₉×#17692, …
maximal normal subgroup of	C₂₉×#8478, C₂₉×#17689, C₂₉×#17692, …
maximal quotient of	C₂₉×#34184, C₂₉×#34215, C₂₉×#34217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2236);

C29×#3504 #16817218