C₂₉×#2010 #16815724

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2010

Subgroups

	subgroup	G/H
center	C₄×C₂₉	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂×C₂₉	#392
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

394 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 88 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)(32,38)(33,41)(34,37)(35,39)(36,43)(40,45)(42,44);(30,32)(31,35)(33,42)(34,40)(36,45)(37,44)(38,41)(39,43);(35,44)(38,45)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7396, C₂₉×#7397, C₂₉×#12114, …
maximal normal subgroup of	C₂₉×#7396, C₂₉×#7397, C₂₉×#12114, …
maximal quotient of	C₂₉×#9938, C₂₉×#9939, C₂₉×#9940, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 742);