C₂₉×#2061 #16815775

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2061

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂³×C₂₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

230 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7442, C₂₉×#12235, C₂₉×#12237, …
maximal normal subgroup of	C₂₉×#7442, C₂₉×#12235, C₂₉×#12237, …
maximal quotient of	C₂₉×#10568, C₂₉×#10569, C₂₉×#10571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 793);