C₂₉×#3104 #16816818

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#3104

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂³×C₂₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(32,35)(33,34)(36,37)(38,39,42,45)(40,46,48,53)(41,49,51,44)(43,50,52,47);(31,34)(35,37);(38,40,42,48)(39,43,45,52)(41,50,51,47)(44,53,49,46);(30,32,33,36)(31,35,34,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8990, C₂₉×#9048, C₂₉×#9232, …
maximal normal subgroup of	C₂₉×#8990, C₂₉×#9048, C₂₉×#9232, …
maximal quotient of	C₂₉×#20734, C₂₉×#21119, C₂₉×#21358, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1836);

C29×#3104 #16816818