C₂₉×#1705 #16815419

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₂₉×#1705

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
prime radical	C₂₉×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 45 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)(35,37)(39,42)(40,44)(43,45);(30,31,32,34,33,35,36,37);(38,39,40,42,41,43,44,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7535, C₂₉×#12364, C₂×C₂₉×#1705, …
maximal normal subgroup of	C₂₉×#7535, C₂₉×#12364, C₂×C₂₉×#1705, …
maximal quotient of	C₂₉×#8813, C₂₉×#9819, C₂₉×#9820, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 437);

C29×#1705 #16815419