C₂₉×#1544 #16815258

order	3712
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1544

Subgroups

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

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8242, C₂₉×#8244, C₂₉×#8246, …
maximal normal subgroup of	C₂₉×#8242, C₂₉×#8244, C₂₉×#8246, …
maximal quotient of	C₂₉×#7564, C₂₉×#7568, C₂₉×#7646, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 276);

C29×#1544 #16815258