C₂₉×#1526 #16815240

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×#1526

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

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

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)(31,35,36,37)(38,39,42,45,43,40,41,44);(30,31)(32,35)(33,37)(34,36)(38,40,43,39)(41,45,42,44);(30,32,34,33)(31,35,36,37)(38,41,43,42)(39,44,40,45)

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×#7570, C₂₉×#7632, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 258);

C29×#1526 #16815240