C₂₉×#1372 #16815086

order	3712
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#1372

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	D₈
commutator	C₈	C₂×C₈×C₂₉
Frattini, cosocle	C₄×C₈	C₂²×C₂₉
socle, prime radical	C₂²×C₂₉	#107
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₄²×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 2 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)(30,31,32,34,33,35,36,37)(39,43)(40,47)(41,48)(44,49)(45,53)(46,52)(50,51);(38,39,44,53,41,45,40,43,42,46,47,51,48,50,49,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7385, C₂₉×#7386, C₂₉×#7446, …
maximal normal subgroup of	C₂₉×#7385, C₂₉×#7386, C₂₉×#7446, …
maximal quotient of	C₂₉×#7101, C₂₉×#7154, C₂₉×#7463, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 104);

C29×#1372 #16815086