C₂₉×#1712 #16815426

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²×C₈

Aliases

direct product

C₂₉×#1712

Subgroups

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

280 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)(32,35)(36,37)(39,42)(40,43)(44,45);(30,31,35,37,33,36,32,34);(38,39,43,45,41,44,40,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7096, C₂₉×#7529, C₂₉×#12310, …
maximal normal subgroup of	C₂₉×#7096, C₂₉×#7529, C₂₉×#12310, …
maximal quotient of	C₂₉×#8818, C₂₉×#9824, C₂₉×#10304, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 444);

C29×#1712 #16815426