C₂₉×#1708 #16815422

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

Aliases

direct product

C₂₉×#1708

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

190 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)(32,36)(35,37)(38,39)(40,46)(41,49)(42,44)(43,47)(45,50)(48,52)(51,53);(38,40,41,47,42,48,50,53)(39,43,45,46,44,51,49,52);(30,31,32,34,33,35,36,37)(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×#7536, C₂₉×#12365, C₂×C₂₉×#1708, …
maximal normal subgroup of	C₂₉×#7536, C₂₉×#12365, C₂×C₂₉×#1708, …
maximal quotient of	C₂₉×#8815, C₂₉×#9819, C₂₉×#9820, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 440);

C29×#1708 #16815422