C₂₉×#1747 #16815461

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₂₉×#1747

Subgroups

	subgroup	G/H
center	C₈×C₂₉	C₄²
commutator	C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂×C₂₉	#376
prime radical	C₂³×C₂₉	#41
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#11769, C₂₉×#11770, C₂₉×#11771, …
maximal normal subgroup of	C₂₉×#11769, C₂₉×#11770, C₂₉×#11771, …
maximal quotient of	C₂₉×#8137, C₂₉×#8138, C₂₉×#8139, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 479);

C29×#1747 #16815461