C₂₉×#1710 #16815424

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₉×#1710

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

168 conjugacy classes of subgroups.

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7093, C₂₉×#12449, C₂₉×#12450, …
maximal normal subgroup of	C₂₉×#7093, C₂₉×#12449, C₂₉×#12450, …
maximal quotient of	C₂₉×#8816, C₂₉×#9821, C₂₉×#9823, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 442);

C29×#1710 #16815424