C₂₉×#2050 #16815764

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2050

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂×C₂₉	#394
prime radical	C₂₉×#575	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

266 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 45
transitive degree	μ_t(G) = 464

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7414, C₂₉×#7415, C₂₉×#12173, …
maximal normal subgroup of	C₂₉×#7414, C₂₉×#7415, C₂₉×#12173, …
maximal quotient of	C₂₉×#10456, C₂₉×#10457, C₂₉×#10458, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 782);