C₂₉×#1921 #16815635

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₉×#1921

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 49 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)(30,31,33,32)(34,35)(36,39)(37,38)(40,41)(42,43,44,46)(45,47,49,48);(30,32,33,31)(35,38)(39,41)(43,46)(47,48);(34,36,37,40)(35,39,38,41)(43,47)(45,49)(46,48)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1921, C₂₉×#21032, C₂₉×#21033, …
maximal normal subgroup of	C₂×C₂₉×#1921, C₂₉×#21032, C₂₉×#21033, …
maximal quotient of	C₂₉×#9536, C₂₉×#9540, C₂₉×#10807, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 653);

C29×#1921 #16815635