C₂₉×#1709 #16815423

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₂₉×#1709

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
prime radical	C₂₉×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

212 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)(31,32)(33,34)(36,37)(38,39)(40,46)(41,49)(42,44)(43,47)(45,50)(48,52)(51,53);(30,31,34,36,35,37,33,32)(38,40,41,47,42,48,50,53)(39,43,45,46,44,51,49,52);(30,32,33,37,35,36,34,31)(39,44)(43,51)(45,49)(46,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7092, C₂₉×#7530, C₂₉×#7531, …
maximal normal subgroup of	C₂₉×#7092, C₂₉×#7530, C₂₉×#7531, …
maximal quotient of	C₂₉×#8816, C₂₉×#9822, C₂₉×#9824, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 441);

C29×#1709 #16815423