C₂₉×#1452 #16815166

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₉×#1452

Subgroups

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

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(35,37)(38,39,41,44,42,45,48,51)(40,43,47,50,46,49,52,53);(30,31,32,35,33,34,36,37)(38,40)(39,43)(41,47)(42,46)(44,50)(45,49)(48,52)(51,53);(40,46)(43,49)(47,52)(50,53)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7147, C₂₉×#7197, C₂₉×#7198, …
maximal normal subgroup of	C₂₉×#7147, C₂₉×#7197, C₂₉×#7198, …
maximal quotient of	C₂₉×#7843, C₂₉×#7849, C₂₉×#8133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 184);

C29×#1452 #16815166