C₂₉×#1713 #16815427

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₉×#1713

Subgroups

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

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7097, C₂₉×#7098, C₂₉×#7532, …
maximal normal subgroup of	C₂₉×#7097, C₂₉×#7098, C₂₉×#7532, …
maximal quotient of	C₂₉×#8818, C₂₉×#9823, C₂₉×#9825, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 445);

C29×#1713 #16815427