C₂₉×#2102 #16815816

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#2102

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂×C₂₉	#400
prime radical	C₂³×C₂₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

158 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 72 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)(30,31,34,33,35,37,39,43)(32,38,40,45,41,42,44,36);(30,32,39,40,35,41,34,44)(31,36,43,38,37,45,33,42);(30,33,34,37,35,43,39,31)(32,38,40,45,41,42,44,36)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7440, C₂₉×#7441, C₂₉×#12307, …
maximal normal subgroup of	C₂₉×#7440, C₂₉×#7441, C₂₉×#12307, …
maximal quotient of	C₂₉×#10687, C₂₉×#10688, C₂₉×#10689, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 834);