C₂₉×#1718 #16815432

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₉×#1718

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

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

normal subgroups only

This group has 164 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) = 61
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 61 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)(30,31,34,37)(32,38,39,45)(33,41,42,36)(35,43,44,40)(46,47)(48,54)(49,51)(50,58)(52,56)(53,57)(55,60)(59,61);(30,32,33,40,34,39,42,43)(31,35,36,38,37,44,41,45)(47,51)(52,59)(53,58)(54,60);(32,39)(35,44)(38,45)(40,43)(46,48,50,56,49,55,57,61)(47,52,53,54,51,59,58,60)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1718, C₂₉×#19613, C₂₉×#19620, …
maximal normal subgroup of	C₂×C₂₉×#1718, C₂₉×#19613, C₂₉×#19620, …
maximal quotient of	C₂₉×#8821, C₂₉×#9826, C₂₉×#9828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 450);